How long can a unit stay on over watch for?

Barring special exceptions (see the Schocktruppen's equipment) a character may stay on overwatch till they use their overwatch attack or the end of the game turn (i.e. after all characters have activated).

Can I attack then place the same unit on over watch?

Sorry, you can't. Your opportunity to place characters on overwatch is before the actual action phase unless there are special abilities involved. Even then, placing a character on overwatch will cost his action, McNeal's medal for example.

cool i apreciate it!