2 questions:
1) In the time of troubles, only part of a diety worshiped on multiple worlds would have been brought down to the walk the earth, right? If they died, would they rejoin the rest of themselves, or would the god permanetly loose that part of their power.
This is one of those paradoxical situations... What probably happened is that Lolth's avatar was sent to Toril, and the rest of her "divinity" was barred from influencing Toril by Ao.
2) Is their ranking (whether their a lesser, intemediate or greater power) based on their total power on all the worlds their worshiped or just the given world?
The power of a deity on Toril is determined by just their worshipers on Toril. Though Lolth on Toril and Lolth on Oerth are the same deity, there are actually differences between them and what power they possess - for instance, on Toril, Lolth has six domains, while on Oerth she only has four... But Lolth on Oerth will have extra salient divine abilities, because the Toril Lolth has had to use three of hers on extra domains, while Oerth Lolth only had to use one. (If that makes sense at all. )