1+2) Dwarves should keep it fed if it isn't a [GRAZER], which grizzly isn't. You can release it by choosing (b)uild-cage(j), slapping it down somewhere, and attaching it to a lever (3 mechanisms), after which you can assign it to a dwarf or put it to a pasture (i-draw fitting pasture-n-use shift+n- search freed bear and press enter).
3) caravan brought animals are perma-trained so no problem there
4) putting them to same pasture somewhat close proximity from each other? This I am unsure of, there has been some changes I've glazed over since my last more active times.
5) yes, no, and yes. Visitor's animals are, if I am guessing right, guinea pigs and rabbits and somesuch small herbivores? They won't be fed by dwarves, and thus tend to starve when their party animal owners get to year long hammertime in your tavern.
6) I've never used animals much for other than part of operation Delay the Clown Parade in which they are woefully underpar. One could, perhaps, use them as gladiatorial animals vs captured and disarmed and/or unarmored goblins/elves/humans, or as bottom layer of drop trap, or just assign them to soldiers as pets, so that they wade into combat with them and go to raids with them. Notable thing is also that giant grizzlies are frigging huge, so in emergency they yield a metric f-ton of meat and bones. Not to be used willy nilly, since they grow relatively slow.