Matakishi's Tea House

1.My green stuff sticks more to me than it does to my sculpt.

Not surprising really as Green Stuff is an adhesive- that is, it was designed to stick to things and the highly textured surface of your fingers give it a lot to grab to. High texture means high friction so you need to either sand off your fingerprints or make your fingers 'less sticky' by rubbing them lightly across chapstick, vaseline, or even better a greasy nose or forehead.

2. How to keep small dollies secure.

When using premade dollies I use a wire 'staple' (or two)
When doing single wire sculpts (heads etc) I put jagged bends in the wire to stop spin.

3.I looked through your tutorials but I could not seem to find how long to bake the clay.
I was also wondering if you could recommend a paint that will last on a figure after being played with a lot, I'm trying to sculpt an action figure out of clay.

What materials are you using to sculpt with? If you are using 'green stuff' it will harden on its own in a few hours. If you want to speed the hardening (called 'cure' time) then just use a light bulb oven with very LOW temp.
If you are using a Sculpey type clay they usually need about 30 mins for a 1" thick bit, so a thin figure may only need 5-10 minutes. I'm not sure using a cork would be safe though so you may want to gently remove the figure from the cork- use some tinfoil to support the figure when it is in the oven.
Any paint will work. Most paints dont last well when handled though so what I would recommend is a really good sealant- varethane spray paints are good because it is literally a plastic coat.
If you are making an action figure you want to play with I would not recommend the Sculpey instead I would use Green Stuff and maybe even some Tamiya Epoxy putty mixed in- this will make the figure VERY durable.

4.Any recommendations for a certain kind of wire to use as a skeleton?

Well if you are just starting out you will want a thicker wire as it is less likely to bend. I use a lot of 16ga and 18ga floral wire, it is super cheap, found in most (womens) hobby stores, and comes straight (coiled wire is hard to straighten out I find). Walmart has it as well as many dollar stores. For really small scale stuff 6mm-15mm I use a thinner wire- 20-22ga floral wire. (for wire the higher the number the thinner/weaker the wire on average).