1: Have some rope reed, pig tails, or silk. If you're starting with rope reed or pig tails, you need to build a farmer's workshop and queue up a 'Process Plants' job. This will get you thread.
Once you have thread (either plant or silk, it doesn't matter) you need to weave it into cloth at a loom. Once you have cloth, you need to queue up a job at a clothier's workshop to make bags or socks or shirts or whatever.
2: Dwarves generally won't eat trapped vermin unless they're starving. A few dwarves with odd tastes might, but as a general rule, vermin is a last resort food.
3: Build a farmer's workshop and queue a 'Milk large creature' job. Obviously you need a milkable creature to do this. If it's not working then all the milkable animals may be outside the burrow assigned to the milker, or you may not have enabled the milking labor on any dwarves.
4: Dwarves don't seem to want to butcher anything dead unless it's RIGHT NEXT to the butchery, and even then it seems to be iffy. I don't know why, but someone else might be able to help. You CANNOT butcher goblins, elves, humans, kobolds, or other dwarves without modding the game.
Cartilage, nervous tissue, and hair have no use and will eventually rot away, but you can have your bonecarver make stuff out of hooves (via the "make horn crafts" job.)
You can't put anything besides your own dwarves or their pets in coffins.