Are we born on this Earth because of our personal kamma?

In ultimate reality, there is no man or woman. There is only Nama and Rupa. Nama is feeling, perception, intention, contact, & attention. The four great elements, and the form dependent on the four great elements: This is called Rupa. It is Nama and Rupa that sends one to hell and Nama and Rupa that prevents one from going to hell. There is a belief in the world that there is the killer and the killed. There is another belief that there is no killer and none that is killed. Both those views are wrong views because there is only Nama and Rupa. If one believed that Nama and Rupa do exist in reality then it is right view. Karma is intention. Intention is part of Nama.

According to SN 15.3, the beginning point of samsara is not evident.

At Savatthi. There the Blessed One said: "From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. What do you think, monks: Which is greater, the tears you have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — or the water in the four great oceans?"

"As we understand the Dhamma taught to us by the Blessed One, this is the greater: the tears we have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — not the water in the four great oceans."

I suggest you practice vipassana instead of thinking about such things. The time is ripe for insight-development leading to Nibbana. You should also check out the biography of Sunlun Sayadaw. http://www.sunlun-meditation.net/ebooks/BIOENG.pdf

The buddha says that sankharas are linked to the kamma of actions and that kamma is linked to various realms. those sankharas, kamma and rebirths can be generated by others or youself

http://obo.genaud.net/dhamma-vinaya/bd/an/04_fours/an04.171.olds.bd.htm#p1

http://obo.genaud.net/dhamma-vinaya/pts/an/04_fours/an04.172.wood.pts.htm#p1

but what matters is ending the sankaras and since puthujjanas are easily influenced by other puthujjanas and non-puthujjanas, puthujjanas should be careful about the humans they associate with.

In case you're interested the way I see it is that something is born -- something physical, biological -- e.g. starting at conception with sperm and ovum etc.

That causes a blastocyst and so on -- which I doubt is a "sentient" being yet, though what do I know?

After (physical) birth the infant develops (psychologically), maybe acquires a sense of "Mum" and "Me" and "Dad" and "Food" and "Cold" and "wet" and so on and so on.

I suspect that ability to distinguish "self" results of acting semi-autonomously (e.g. "if 'I' start to cry, then Mum arrives") -- eventually the whole DO cycle, e.g. "I've learned I prefer the feelings associated with Mum being here, maybe feelings of needs (and eventually "cravings") satisfied, therefore I want Mum to arrive, therefore I intend to cry".

People (on this site) interpret "birth" and bhava and so in different ways, but I think that this (above) is at least one or two of those ways (i.e. physical birth plus the arising of a self-view or conceit, plus kamma as an intentional action, resulting from previously acquired/stored/interpreted/associative experience).

This is further complicated by two factors:

• This answer associates a self (i.e. "I" or "we") e.g. with physical form, a body (which anatta may suggest is a wrong view and/or well worth unlearning)
• There's more to a person (and a person receives more from their parents) than just DNA -- also food, a formal education, all informal experiences -- and not only from "parents" but from teachers, friends, the world -- and from "themselves" i.e. people are shaped by "their own intentions/actions"

Why were we physically born?

That's biology, isn't it? So e.g. "ask your Mum and Dad" about that?

Or do you mean, "why do 'we' associate 'me' with 'this body' or 'our body'"? In which case, I don't know, I think there was a metaphor in a sutta of "a dog, tied to a stake"...

Was it our personal kamma? Did we personally choose this?

I think it's better not to blame other people -- e.g. "you made me like this, you made me do this, it's your fault that I exist" and so on.

Does kamma create the self (person)? Or does self (the person) create kamma?

So far as I know, the text says that "people inherit their own kamma".

Also I think the Dependent Origination is taught as a (repeating) cycle, a.k.a. "the wheel of life".

Did the Buddha teach it cannot be determined whether the chicken comes before the egg or the egg comes before the chicken?

It's "a beginning is not evident", isn't it?

Is this why many Buddhists are vegetarians?

Well ... indirectly? Perhaps?

There are personal reasons, but I don't know that I can attribute those (project them onto) "many Buddhists".

That kind of doctrine (vegetarian) is more a feature of some schools than others.

I think the Buddha in the suttas says more about e.g. "gratitude and parents" than about "chickens and eggs" (though "not killing" and "metta" and so on is also, I think, clearly mentioned).

The answer comes in DN 15:

"Thus, Ananda, from name-and-form as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-and-form. From name-and-form as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging. From clinging as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, aging, death, sorrow, lamentation, pain, distress, and despair come into play. Such is the origination of this entire mass of stress.

It's not because of kamma that we're born.

The cyclic link between name-and-form and consciousness, may be the clue to why a beginning is not evident, just like the chicken and egg.