93 Sc300 Got A Few Probs

[Snaxx843]

hey i just bought a 93 sc300 with a 5 speed this is my first lexus an my first manual im having sum probs with it an was hoping to get some info that could help first my battery light is on i thawt is was just the battery so got a new battery an the light was still on so i think its my alternator also my car has white smoke coming out of the tail pipes the engine light is not on it runs rough but the funny part about that is that the smoke doesnt happen all the time sometime it will smoke an sum times it wont i dont know what to do