Before I get into the Zen part of this question, I'm going to lay out an assumption. By "direct seeing" I'm assuming that you are referring to abhijna which is more often translated as "direct knowing". This direct knowing includes knowledge of the destruction of the taints, beings arising and passing away according to their karma, recollection of past lives, the uprooting of ignorance, etc. If that's what you are referring to, then no, beginners mind is more mundane than that.

You also use another phrase - clear comprehension. In the mindfulness teachings of the Pali canon, this is the most commonly used translation of the word sampajanna. This is most often taken to mean full awareness of an action. If you are raising an arm, you are aware that you are raising an arm, when you are walking, you know that you are walking, etc. This is getting a little closer to what is meant by beginners mind.

So what is beginners mind, then? One way you might be able to get a handle on the concept is to think back to when you first started learning something. We'll take driving a car for example. During those first few times you drove, there was a sense of heightened awareness. You probably remember everything about that experience - who you were with, what street you were driving down, etc. You were extremely conscious of what your feet were doing, how you were holding your hands on the steering wheel, and so forth. Your mind was in a place of novelty and immediacy. It didn't wander very far from the task at hand. It didn't devolve into conceptualizations about "driving theory" or other cars that you had driven before. The more times you drove, the less immediacy that experience had for you. Over time, you eventually started taking the whole thing for granted.

The Zen mind is always at the beginning. To lose that immediacy is to fall into duality and conceptualization. Practically speaking, you can work on developing that kind of awareness. That's really the thrust of all mindfulness practices (and I HIGHLY recommend Ven. Analayo's Satipatthana). Don't try and imagine what it would be like to see something as if you were just born. Just be aware of what you are doing - thoughtlessly yet attentively.

Base Direct Seeing (Kamma Sammādiṭṭhi)

Realizing/thinking of kamma system, wholesome actions and wholesome resultants of wholesome actions & unwholesome actions and unwholesome resultants of unwholesome actions, after know anything by any senses.

Concentration Direct Seeing (Jhāna Sammādiṭṭhi)

Realizing/thinking of jhāna system, wholesome minds and wholesome resultants of wholesome minds & unwholesome minds and unwholesome resultants of unwholesome minds, after know anything by any senses.

Access To Insight Direct Seeing (Vipassanā Sammādiṭṭhi)

Realizing/thinking of paticcasamuppāda system, causes of whole suffering (5 aggregates), after know anything by any senses. This viewing will lead to see 3 characterizes.

Note: I understand whole tipitaka-pali without cutting anything off, because I use this 6, the other 3 is for ariya, sammādiṭṭhi that summary from tipitaka by commentary.

What is direct seeing?

It is your second option. As you said:

a beginner starts by watching meditation objects "imperfectly" with all the concepts of each meditation object mixed with what really is and then slowly through continuous practice the meditator will be able to understand what is concept and what is direct experience.

What is beginner's mind?

Beginner's mind is obviously not actual beginner's mind, it is the clarity you get when you let the dust settle down either through meditation or by creating some distance between yourself and the situation. It is when you are not bogged down with too many details, perspectives and ambiguities but see the configuration of the situation with clarity.

The difference between the two.

The two are related, in both cases we talk about experience or perception. But the contexts are different, in case of Direct Seeing we are talking about someone starting with conceptual map and then finally "getting it" for real. While in the case of Beginner's Mind we are talking about someone starting with ambiguous experience and then attaining clarity. The end result is the same but the starting points are different.

I don't think you put effort into Beginner's Mind. It comes by itself as a result of not proliferating the intoxication, not feeding the fire, the dust settling, the distance growing or whatever other metaphors you want to use. It's the effort of not-doing, not the effort of doing.

Direct seeing on the other hand does require effort. This effort is known as Vipassana or Inquiry or Insight into your direct experience, guided by the conceptual map of Dharma.

Think you messed up two unrelated terms that's why it added unnecessary confusion.

Beginner's Mind (初心):

It's for depicting the Buddhist, the seer, when at the 1st moment drawn to the Dharma, knowing there is a way out for this world and a mean for perfect liberation, the elation, joy and dedication. Like the newly wedded. But it will decline gradually, the newly wedded becomes old couples, boring, mandatory... So is the Buddhist, the seer. A Ch'an tagline: the 1st year, at the heart is the Buddha; 1 year later, he's at the door; 3rd year, at the other side of the azure (佛在天邊). And also, when Buddhist becomes old greasy, he is prone to be drown in the sea of Dukkha, suffocated by the wheel of Anicca, intoxicated by the liquor of Nibbana... he can't maintain proper thinking for his mind has been invaded and dissected by Buddhist Jargons, or/and, faking Jhanas like faking Ogsms.! :D. Like you said, only the words about how kiwi taste but never ever have a bite on it, tasting it himself. The worst is, he even starts to teach others how kiwi taste like.

Direct Seeing:

It has multiple meanings, depends on what level you are talking about. As I assumed you asked for trying to get hints about how to have advance vision of things - the thing of itself, not thing of concept (it's my cumsy way to depict your concern). Grossly I would say DS can only happen on the level of 7 Vijnana and the 8th. Below are the 6, most of us using conscious or unconsciously the 5 Vijnanas, some can use the 6 - 6th sense. The 5 are faculties of info inputing, the 6th, apart from managing the input info, also is able to draw past info, still, it works on info - concepts. The 7th is more pure, it's purely intention. The 8th is the Sea, the Reservoir, the Treasure House... For anything coming down it has to go passing the 6th, becomes concept, to become Form in this world. So, the task for the seer is to stop the interference of the lower 6, access the 7th then the 8th... If you can, you are able to do DS.

My dear friend in Dhamma, @UUU… I sincerely hope that you try to understand what I write. Both you and I have a lot of un-learning to do. Today a relatively small group of dhamma farers are seeing dhamma in a new light, practicing it and getting very favourable results. I joined such a group, a month ago, and experienced the same. I was able to go to the four basic levels of jhana with ease. Most of what I’ve written, and what others write as answers in this forum are true only at a mundane level. When I told of this last week in this SE forum, I was told that in Pardes (Jewish exegesis) too there is a higher level of meaning.

In pardes, the term, sometimes spelled PaRDeS, is an acronym formed from the same initials of the following four approaches:

Peshat — "surface" ("straight") or the literal (direct) meaning.
Remez— "hints" or the deep (allegoric: hidden or symbolic) meaning beyond just the literal sense.
Derash— from Hebrew darash: "inquire" ("seek") — the comparative (midrashic) meaning, as given through similar occurrences.
Sod (pronounced with a long O as in 'soda') — "secret" ("mystery") or the esoteric/mystical meaning, as given through inspiration or revelation.

Thus, Sod represents the hidden meaning. Similar to this, the hidden meanings of many words have come to light in the recent past. So, to come to your question proper…

Direct seeing can happen if ever you get to discuss the Dhamma with someone who is fully established in the Path. For that, he or she has to be at least a Sotapanna (a stream entrant). Then you must develop a trust in what that person tells you – a trust that is unflinching. A connection is made between the two where the five Hindrances (nivarana) are kept at bay. ‘Direct Seeing’ happens at such a moment. It is a ‘vi-nivarana moment. It is a moment devoid of the five hindrances. At such a moment, that person can help you become a Sotapanna (a stream entrant) too.

Every person, animal or plant emanates an aura or human energy field which is a colored emanation. The rays that a Sotapanna (a stream entrant) radiates has a captivating effect when that trust is built between the two. Once you too gets established in the path, mentally you become distant from the ways of the world (world = Lokha). Then in meditation you experience 'Aloka' - radiant light. In the fourth Jhana, this radiant white light engulfs your whole body - a truly beautiful experience to have- it is bliss.

When a Sotapanna begins to meditate, he/she can easily suppress the five hindrances, and get to experience direct seeing. How to recognize a sotapanna would be your next question.

If a person tells you that it is INCORRECT to say that anicca, dukkha, anatta is impermanence, suffering, and “no-soul” or “no-self”, then there is a greater possibility that he/she is a Sotapanna. That person will tell you that the correct meanings are, respectively: there is nothing in this world that can be maintained to one’s satisfaction, (therefore) suffering arises, and (therefore) one is truly helpless in this world. If you start to see this by contemplating on this, it will not be too long before you too will experience “Direct Seeing”.

Now let us try to understand what this “beginners mind” means as per the Dhamma. The Pali term for ‘beginners mind’ is called “pabhassara citta”. A better term for it in the English language is ”Radiant/Luminous Mind”. When meditating what we desire is a mind that generate and maintain a citta at the level of the “radiant mind”.

Any given persons initial thought is a pabhassara citta, but gets contaminated no sooner it comes into being because of our “abhi-Sankhara”. Our monkey mind can never be without being in the Vitakka/Vicara mode. In meditation, after the first jhana one can go beyond the Vitakka/Vicara mode to the Avitakka/Avicara or Savitakka/Savicara mode. These states are without discursive thinking (vitakka/vicara). When one gets to the fourth jhana, s/he gets to experience the Radiant/Luminous Mind.

The process of contamination of a citta is found in the Pabhassara Sutta in the Anguttara Nikaya. The Sutta says that, “Bhikkus, citta (the first stage) is pabhassara until “upakilesa” or defilements are introduced, when one starts to think through this initial thought, thereby leading to “upakilitta” or contamination. Those “puthujjano” who do not understand this, cannot comprehend the reality (yathabhuta). Therefore “therefore, Buddha does not recommend citta bhavana to them.

There are two types of citta bhavana. They are the Avitakka-Avicara Bhavana, and the Savitakka-Savicara Bhavana. These two are Ariya meditations. In the other type (the Anariya meditations), one can focus on any object; in the Ariya Meditations one focuses on Nibbana. Thus, vitakka, vicara for Anariya samatha meditation becomes savitakka, savicara, emphasizing the focus on Nibbana.

Am I wrong or is "beginner's mind" a Zen term that means "seeing the experience you are aware of, moment by moment, as if you have never experienced concepts before... Like you have just been born with a mind that has not developed concepts yet and so you see things as they really are?

Yes, this is wrong because it has already jumped ahead into the future with a conception of achievement (even though that conception of achievement is non-conceptual seeing). This question is already saturated in dogma & ambition.

Is "Beginner's Mind" equivalent to direct seeing or very related to direct seeing(or even clear comprehension)? Should insight meditators be "trying" to see this way, "trying" to see things as if the meditator was just born? ...OR...

OMG! This is even worse, when saying: "trying to see things". Zen Master big whack with big stick!

The pure mind automatically sees things clearly. The role of beginners mind is to allow the mind to see clearly (similar to pulling up an anchor so a boat can float freely down a river).

Does direct seeing develop when a beginner starts by watching meditation objects "imperfectly" with all the concepts of each meditation object mixed with what really is and then slowly through continuous practice the meditator will be able to understand what is concept and what is direct experience?

No. Direct seeing develops when the mind is free from thoughts, hindrances, concepts and, most of all, ambition.

It is simply not good enough to focus the mind with strength. Instead, for direct seeing to start, the mind must abandon ambition (craving) for concentration.

If this is true then its not a matter of effort or trying to see direct reality but more about "discerning" what are concepts and what is the real object that is arising in experience by just seeing what the meditator sees. Maybe, I'm mistaken somewhere because it's not totally clear to me.

To examine water clearly & directly, you cannot take a microscope into the waves of the ocean because you will be washed around by the waves. Instead, you must take a drop of water and place it quietly with stillness under a microscope.

Similarly, first the mind must be stabilised with (wrong) concentration. Then any intention or ambition to concentrate must be abandoned to manifest right concentration or flexible stillness. Then right concentration, without an act of will, will see things directly.

Therefore, beginners mind is to meditate without any ambition; as though you are completely virgin & innocent. Intellectual dogma about 'non-conceptualization', 'no-things' & 'no-inherent-existence' is not beginners mind.

In the Theravada tradition, we learn Yoniso Manasikhara. It means paying wise attention. And the knowledge or vision gained by paying wise attention is called the Yathā Bhūta ñāna Dassana or the vision of manifestations in their real form.