1. The one you're in, permanently.

3. You can't use skills that are unique to a class (any skill with an open palm as the icon, for example Afternoon Tea from the Maid class) when reincarnating in another class.

thanks for answering questions one and three @Z3n

For the 2nd question, team attack chances differ for each unit to another. While they have a fixed base value, you can increase/decrease the odds depending on a few factors, such as which weapons the attacking unit has, whether the units have a master/student relationship, and whether the other allies moved and/or performed an action before triggering the team attack. You can check a list for team attack chances here[gamefaqs.gamespot.com] (keep in mind that the table isn't updated to include the characters from the remakes, but it should still cover most characters). Adell and Rozalin are an exception to the rule, they increase the odds of performing a team attack with chapter progression (though there seems to be a bug in this version of the game that might lower the chances).

Adding to what Z3n said on the 3rd question, while you can transfer generic skills, you still need to beware of them to not dropping below lv1 (and maybe its respective level of weapon mastery) when reincarnating. Also, I think the open palm icon/maid example is from D5? Though I suppose it still gets the point across.