Well it was Serbia and Montenegro before that. Since the country split into 2 I guess they let them chose. It's not exactly the same situation as Switzerland and Kosovo.
Right. I think if a player is born in a country that hasn't formed an NT yet (for e.g. a player born in Kosovo, but grew up in Belgium and represents the Belgian NT) CAN play for Kosovo, even though he might have represented another country beforehand. I'm pretty sure thats the rule.
EDIT: This from wiki: In international football, players can normally only play for one national team once they play in all or part of any match recognised as a full international by FIFA. However, an exception is made in cases where one or more newly independent states are created out of a former state. Based on current FIFA rules, a player will be eligible to play for Montenegro, even if he had previously represented Serbia and Montenegro or any other country, if at least one of the following statements applies:
He was born in Montenegro.
At least one of his parents and/or at least one of his grandparents was born in Montenegro.
He has lived in Montenegro continuously for any two-year period.