There is one of each god, and most gods are drawn to worlds where they have worshipers. Asmodeus, for example, has worshipers on many worlds. Some gods, like Tiamat, adopt different names on different worlds. #wotcstaff

Yes. Over the centuries, there's been enough traffic between the worlds/spheres that deities of Oerth and Krynn have followers in Toril (and Abeir), and vice versa.

Judging by the frequency with which Elminster shows up at my various back doors, and drops casual comments about what he saw, experienced (and mainly drank and ate) at historical Earth times and events, I'd say Earth and Toril have been constantly connected for a long, long time.

This begs a question. Is there any explanation for the time jump? I mean, one day Earth and Faerûn were conected at year 1372, the other day in Faerûn 100 years had passed. Was the speed of the... Um, "timeline conection" affected by the Spellplague as well?