Form in the formless realms

Dependant Origination declares that from Consciousness (Viññana) arises Nāma-Rūpa, not just Nāma. Therefore it is implied that even in formless realms the entities that exist there also have a form of some kind.

No, there's no implication there. While it's true that the suttas stated that Vinnana is the condition for the arising of Nama-Rupa, nowhere in the entire Canon did it say both Nama and Rupa must always arise together throughout the 31 planes of existence!

Question 1: Why couldn't Buddha teach the Dhamma to Uddakka Ramaputta and Alara Kalama.

Couple reasons: 1. Those teachers already passed away 2. Those beings born into the ARupa realms do not have Rupa (ie. no physical eyes, ears, etc) hence would not be able to receive the Buddha's Teaching.

Question 2: What is the difference in form between the Rūpa Lōka and Arūpa Loka.

In Rupa realms, there's still some sort of fine/subtle materiality, while in ARupaLoka, there is no Rupa at all. Refer to 31 Planes of Existence for further infos.

OP: Question 1: Why couldn't Buddha teach the Dhamma to Uddakka Ramaputta and Alara Kalama.

The reason for this is that they had already passed away at the time of the Buddha's enlightenment.

From MN 26:

"Then the thought occurred to me, 'To whom should I teach the Dhamma first? Who will quickly understand this Dhamma?' Then the thought occurred to me, 'This Alara Kalama is wise, competent, intelligent. He has long had little dust in his eyes. What if I were to teach him the Dhamma first? He will quickly understand this Dhamma.' Then devas came to me and said, 'Lord, Alara Kalama died seven days ago.' And knowledge & vision arose within me: 'Alara Kalama died seven days ago.' The thought occurred to me, 'A great loss has Alara Kalama suffered. If he had heard this Dhamma, he would have quickly understood it.'

"Then the thought occurred to me, 'To whom should I teach the Dhamma first? Who will quickly understand this Dhamma?' Then the thought occurred to me, 'This Uddaka Ramaputta is wise, competent, intelligent. He has long had little dust in his eyes. What if I were to teach him the Dhamma first? He will quickly understand this Dhamma.' Then devas came to me and said, 'Lord, Uddaka Ramaputta died last night.' And knowledge & vision arose within me: 'Uddaka Ramaputta died last night.' The thought occurred to me, 'A great loss has Uddaka Ramaputta suffered. If he had heard this Dhamma, he would have quickly understood it.

The sutta proceeds with the Buddha selecting the five monks at the Deer Park at Isipatana, to be his first disciples. They are the ones who attended to him when he practiced extreme asceticism.

OP: Question 2: What is the difference in form between the Rūpa Lōka and Arūpa Loka.

If you mean the traditional Buddhist cosmology of the 31 planes of existence, please see the AccessToInsight page on The Thirty-One Planes of Existence:

The Immaterial World (arupa-loka). Consists of four realms that are accessible to those who pass away while meditating in the formless jhanas.

The Fine-Material World (rupa-loka). Consists of sixteen realms whose inhabitants (the devas) experience extremely refined degrees of mental pleasure. These realms are accessible to those who have attained at least some level of jhana and who have thereby managed to (temporarily) suppress hatred and ill-will. They are said to possess extremely refined bodies of pure light. The highest of these realms, the Pure Abodes, are accessible only to those who have attained to "non-returning," the third stage of Awakening. The Fine-Material World and the Immaterial World together constitute the "heavens" (sagga).

The Sensuous World (kama-loka). Consists of eleven realms in which experience — both pleasurable and not — is dominated by the five senses. Seven of these realms are favorable destinations, and include our own human realm as well as several realms occupied by devas. The lowest realms are the four "bad" destinations, which include the animal and hell realms.

The details of all 31 planes are on that page.

OP: Dependant Origination declares that from Consciousness (Viññana) arises Nāma-Rūpa, not just Nāma. Therefore it is implied that even in formless realms the entities that exist there also have a form of some kind.

If you look at that page, it says that unconscious beings (asaññasatta) who are on plane #22 have body but no mind. On the other hand, the top four types of beings in the arupa-loka have mind, but no body.

Doesn't that conflict with the definition of name-and-form in Dependent Origination?

My take on it is that the Dependent Origination taught in the Pali suttas applies to humans, and any beings with both body and mind. The Buddha, being a pragmatic teacher, targeted this teaching only at those who are able to listen to it and understand it. This does not include the unconscious beings (asaññasatta), those beings in the arupa-loka, and also the beings who are in the state of deprivation (apaya).

There may be more to Dependent Origination as in how it may apply to those beings with mind and no body, or with body and no mind, but this is one of those things which the Buddha did not teach us because it is not useful to us.

As we see in SN 56.31:

Once the Blessed One was staying at Kosambi in the simsapa forest. Then, picking up a few simsapa leaves with his hand, he asked the monks, "What do you think, monks: Which are more numerous, the few simsapa leaves in my hand or those overhead in the simsapa forest?"

"The leaves in the hand of the Blessed One are few in number, lord. Those overhead in the simsapa forest are more numerous."

"In the same way, monks, those things that I have known with direct knowledge but have not taught are far more numerous [than what I have taught]. And why haven't I taught them? Because they are not connected with the goal, do not relate to the rudiments of the holy life, and do not lead to disenchantment, to dispassion, to cessation, to calm, to direct knowledge, to self-awakening, to Unbinding. That is why I have not taught them.

There is an alternative view to this.

The alternative view is that the 31 planes of existence are just different states of mind, that is to say not a literal physical rebirth into those planes, but rather the momentary rebirth of one's personhood into those planes i.e. entering different states of mind. This is usually supported by the association of the 4 rupa jhanas and 4 arupa jhanas, as well as brahmaviharas with different planes.

This is like a more subtle perspective into the teachings, compared to the one previously mentioned, which is gross.

declares that from Consciousness (Viññana) arises Nāma-Rūpa

It declares that both name & form arise with consciousness as requisite condition. Name and Form are not one and same thing;

"And what is name-&-form? Feeling, perception, intention, contact, & attention: This is called name. The four great elements and the form dependent on the four great elements: This is called form. This name & this form are called name-&-form. [Sn12.2] (https://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.002.than.html)

When form comes into play then 'feeling, perception, intention, contact, & attention' can be delineated.

Form is delineated in as far as perception that arises in dependence on form is delineated, ie what is see by the eye.

Perception can be not dependent on form ie 'space' is a mental conception and in & by itself does not depend on "things", it is not known by it's density, fluidity, aerial nor by a thermal property and it is without shape, color, taste, sound, smell nor a tactile or tangible expression.

Therefore when perception of form fades from the mind, there is then the underlying perception of infinite space.

You need to conceive space to conceive form but you don't need form to conceive of space, therefore underlying. When you have a material thing it has a spatial property [occupies space, is in a space] but space in & by itself doesn't have a material property.

Therefore it is said;

"Friend, what can be known with the purified intellect-consciousness divorced from the five [sense] faculties?"

"Friend, with the purified intellect-consciousness divorced from the five faculties the dimension of the infinitude of space can be known [as] 'infinite space.' The dimension of the infinitude of consciousness can be known [as] 'infinite consciousness.' The dimension of nothingness can be known [as] 'There is nothing.' Mn43

"Further, Ananda, the monk — not attending to the perception of wilderness, not attending to the perception of earth — attends to the singleness based on the perception of the dimension of the infinitude of space. His mind takes pleasure, finds satisfaction, settles, & indulges in its perception of the dimension of the infinitude of space. MN121

Perception of infinite space is different to thinking about space, thinking about space is classed as 'perception of thinking'.