All Palestinians are looking for at this point is some kind of gesture that says to them "we acknowledge that you are human beings" and they haven't been getting it. A two state solution is something many great minds have tried to put together for very many years with little indicating it is going to happen in the near future, but hopefully it does as while it certainly wouldn't fix all the issues in the region it would cool things off a little.
No, a two state solution will not help with regional stability in the Israeli-Palestinian conflict. Both sides believe they are completely right. If both Israel and Palestine are given half the land, they will both think they were half cheated. Thus, the conflict will always continue. This is a very difficult issue and unfortunately there are no easy answers.