1. Is it possible for a creature without hands to be able to pick up weaponry and tools?
No
2. I want each of my castes to have their own names in arena mode (Ex: Hyena man 1, Hyena woman 2, Warg 3, etc) But I have no idea how to make it so in the raws, because whatever I do they still turn out as hyena man 1/2/3. I also have the problem of the warg caste only showing up as female in the arena. That's not as much of a problem, but I would still like to know what's up with that.
The name of the creature in arena mode is just a name, it will not show up in fortress mode. You can change it on an individual bases, but it is unchangeable and impotent as far as the game is concerned.
Do you have a male warg cast? *Looks at Warg*. Oh I see. You need to have male and female as separate casts, you only have one cast, so it won't work.
3. Is it possible for a non intelligent creature (a pet, essentially) to give birth to functional civ members?
Kind of, but it is messy. Hugo was working on something like that. I myself have another kind of walk around, but it is even messier. Hugo's makes your guy give birth to dwarves, but mine basically just transforms them into dwarves.
Basically in my way, you give them a syndrome that turns them into the species you want. They then act like the species, with some glitches, but they can do anything the civ members can like that.