Does hell exist in Buddhism?

I understand that hell is being used for keeping the order of our society

Order of the society is not the goal of Buddhism. The goal is to attain Nibbana -in other words, to end suffering.

Does hell really exist in Buddhism

There are many hells, not one. They are actual realms where beings are born into, due to unwholesome Kamma. Hell-beings experience both physical pain and mental suffering. Hells are categorized into 4 types:

1. Asuras
2. Petas(Ghosts)
3. Tiracchana(Animals)
4. Niraya(Hells of great suffering)

it creates fears instead of freeing one's mind from suffering. It also creates a mechanism of punishment for not believing in the religion

Whether you believe in Buddhism or not, if the Kamma that comes forward to give your next life is unwholesome, it will cause birth in one of the above mentioned hells.

If a doctor advises a patient not to smoke, warning that he could get lung cancer as a consequence, is it a mechanism of punishment for not believing in the doctor?

If it is written in Tipitaka, how do we know that it wasn't added later by someone that wanted to use it as a rule for making people behave themselves?

When you commit an unwholesome act, you can notice how the nature of your mind changes. A part of this Kamma you have to face in this life. It is called Dittadhammavedaniya. If you pay wise attention, you can notice how your life changes according to the Kamma you do. With that understanding, it is not hard to believe that a birth caused by an unwholesome kamma will lead to a bad destination.

If you need visual proof of the actual hells, you have to do Samatha meditation and attain the divine-eye faculty.

Does hell exist in Buddhism?

Yes it does.

how do we know that it wasn't added later by someone that wanted to use it as a rule for making people behave themselves?

No one added it later.
Now I will give my answer.

Even Lord Buddha as mentioned about hell in several suthras. You have to know that Buddhism doesn't accept "the hell" concept. Because according to the preaching there are many hells. Lord Buddha has clearly mentioned about each of the hell including its life span, size of it and the pain creature are suffering. If someone goes to hell after the death, which hell he should be born is decided by the sins he has done. (not only in this life). But Lord Buddha clearly mention that if someone born in hell it's really hard to get out from there.

Please note that there is a good explanation for heavens also.

So my personal idea is try to do good deed as much as you can. If you can to do good deeds at least try to stay away from committing sins.

Please note that in hell, who ever born in there gets a physical body too

Yes. Heaven and Hell exists… But both are impermanent and therefore source of suffering…and therefore one should develop the habit of not clinging to any of these.

Hell exists in Buddhism but not the kind of you normally you think of as hell (examples would be hell in conventional Christianity. *Ancient Christianity/Gnosis is different story)

In fact, you are in hell right now. Heaven and hell exists within you at the same time but you just don't realize. If your life is guided by something imaginary and not own your own and chasing for something imaginary you think is real and suffering by them, wouldn't it be reasonable to call that hell?

How would hell be completely existent in every school of Buddhism if it was a tool added to control society? If something was added not everyone would accept it resulting in various schools as we see now but this hasn't occurred with Hell so it isn't a later addition.

In Buddhism, the word translated as "hell" is 'niraya'.

BSk. niraya, nis + aya of i = to go asunder, to go to destruction, to die,

SN 35.135 contains the Buddha's description of 'niraya' occurring at the six senses bases, similar to the 'Fire Sermon.

MN 130 appears to contain King Yama's description of 'niraya', which appears often mistakenly attributed to the Buddha.

Yes, hell exists in Buddhism as a literal real place as real as this world we live in, but there many hellish worlds and they are temporary (though many can last for extremely long time-periods).

In reality the concept of hell might have originated in Buddhism because early Hinduism does not seem to have the concept nor does early Judaism or the majority of pre-Buddhist religions, they have only vague ideas and concepts.

Buddhism is among the only religion where hell is central concept, described in high graphic details, highlighted and emphasized all the time. Most certainly it was not added in because it is found everywhere in earliest scriptures.

This makes me wonder if NT Christian writers had copied the concept of hell from Buddhism since there were many Greco-Buddhists. The Greek concept of hell is vague and only somewhat like the NT Christian version which seems to more resemble Buddhist hell. It would be much more reasonable to argue that hell was added into NT Christianity than added into Buddhism, because the evidence shows Buddhism as the probable originator of the hell concept.

Which other recorded figure had ever described hell in such high graphic details before The Buddha?

The Buddha says:

"In the same manner bhikkhus, the unpleasantness and displeasure experienced on account of six thousand whips three times a day cannot be reckoned as a comparison, not even as a quarter, nor even as a sign for the unpleasantness and displeasure experienced in hell. The warders of hell give him the fivefold binding." (Balapandita Sutta, MN 129)

"And then later on, with the divine eye, which is purified and surpasses the human, I see that on the dissolution of the body, after death, he has reappeared in a state of deprivation, in an unhappy destination, in perdition, in hell, and is experiencing extremely painful, racking, piercing feelings.

Suppose there were a charcoal pit deeper than a man's height full of glowing coals without flame or smoke; and then a man scorched and exhausted by hot weather, weary, parched and thirsty, came by a path going in one way only and directed to that same charcoal pit.

Then a man with good sight on seeing him would say: 'This person so behaves, so conducts himself, has taken such a path, that he will come to this same charcoal pit'; and then later on he sees that he has fallen into that charcoal pit and is experiencing extremely painful, racking, piercing feelings. So too, by encompassing mind with mind... piercing feelings." (Maha-sihanada Sutta, MN 12)

You said:

"As it creates fears instead of freeing one's mind from suffering. It also creates a mechanism of punishment for not believing in the religion as well."

I don't know, lots of things create fear, but the belief in hell can create positive fear and motivation to act. The Buddha states the truth not what people necessarily want to hear.

My personal belief is that hellish worlds are really physically real and that it would be proven in the future, it's only a matter of time. I already have a hunch on how it could be proven, but who wants to witness or go to hell?

Yes, according to Buddhism, hell exists. Individuals who have accumulated bad karma may be reborn in hell, the animal realm, as ghosts, or even in the human world but with great difficulties. Hell is regarded as a realm of extreme suffering, surpassing any other. Those who have committed very grave karma may be reborn in hell to pay for their actions. Hell can be further divided into realms like "avīci," "raurava," "maha raurava," etc. In Buddhism, the human world, gods, and the Brahma realm are considered "sugati," while the animal realm, demons/ghosts, and hell are considered "duggati."