1) Generally you tell in the embark screen. The biome of the area currently selected appears on the top of one of the side windows, if it's not there press tab until it shows up. As for determining your biome post embark it takes a little detective work. If you have a large number of murky pools it is probably a swamp but weather it's tropical or temperate is a bit harder to determine. That the map doesn't freeze helps, but it could still be a warm temperate. If the change of season announcement sometimes also says something like "the wet/dry season has come" you are in the tropics, otherwise you are probably in a temperate area.
2) Never tried it myself, I would guess changing the dwarves [eat_sapient_...] tags in entity_default to acceptable might be enough, but it might not be, and it could be hard coded at any rate.
3) Yes, the animal has to be native to a biome the civ has access to if you also want it to be available at embark but just adding the [trAINABLE] Tag. It will require a regen, since they know what creatures they have access to from worldgen as well. But it should allow the creature to be trained if you can manage to tame a wild one regardless. For invaders, they need to have it available to their civ and they usually won't bring them for the first few attacks. I have only seen this work back in 2D however. I think there may be something wrong with the invaders bringing pets with the current versions, I haven't seen any in a year of playing.
4) Yes the above applies, with the exception of it not working on the race you are playing, there is no way to tell yer guys to mount up. Make sure they have the mount tag and the invaders have access to their biome. Flying mounts are shaky, sometimes working, sometimes causing the pathfinding bug. Also it will require a regen, since they know what creatures they have access to from worldgen.
5) Try it. It sort of works in adventure mode. But the creature's size usually isn't changed and they don't grow any new bodyparts they should have as the new creature until save and reload. They will get special abilities like firebreath, poison and web though. And yes, companion is probably the best tool for this.
6) In theory yes, in actuality no. Wildlife populations are saved at worldgen. If they didn't live there when worldgen ended they won't live there after a mod.