First of all why would the soul come back? What does
this accomplish?
To learn lessons that are essential to progressing/evolving into a more loving entity.
The situation which surround the soul
change with each life, therefore how does this allow
us to deal with past circumstances.
Ever notice how your "problems" follow you wherever you go? Same thing. The lessons to be faced and overcome can arise in different circumstances, so the important thing is to meet them and overcome them in whatever situation they arise during the current physical life.
He or she comes
back in a different body, with a different brain; therefore
a different person is involved, and that person has not
technically experienced reincarnation.
You are assuming that what you are is limited to the physical mechanism of body/brain. What you are, according to religions that teach reincarnation, is something that transcends those, and the body/brain is just the interface mechanism with the physical world. The deeper "essence" of you is untouched by the physical world, but it's the physical world that is the "playing field" in which the "spirit" (for lack of a better word) learns to face and overcome those lessons which will help it evolve back to unity with its source.
One other question, if one takes his own life will he
or she be reincarnated? If so that create A whole set
of new problems.
Suicide is a way of avoiding facing the lesson being faced, so yes, one would reincarnate.