I read somewhere that it was March 14 but I can't say for sure.
That's not too far off, not bad.
The Dharma Initiative brought the bears to the island and used in electromagnetic energy research. Once they'd been trained (the cages with the fish biscuits at one of the Dharma stations, can't remember the name) they were taken to the Orchid where they were taken to the Frozen wheel to push it and be transported through space and time (rather than having a Human do it and get ripped apart or something)
After the Purge on the Island the ones that survived were set free, and ran into some of the Islanders when they arrived.
Smoke monster? He was originally a normal man, but him and his brother (Jacob) found the heart of the island and were changed. He's the dark side of the island, and Jacob the light so to speak. Faces for the struggle of good vs evil.
I have zero recollection of the others floating