Satin or Gloss finish, which has more protection?

Which finish would have more protection against temperature, humidity and less chance of cracking?

If it's possible, how much would it cost to gloss an already satin finished ukulele?

Neither. The material is identical except for a de-glossing chemical added to make a satin finish. You can probably buff your satin to gloss with elbow grease and a micro-fibre cloth. Try on a small area of the back.

If you simply paint over the current finish, you will reduce the sound because the finish will be very thick, thus restricting the movement of the top. Refinish means removing the original finish and re-applying a new coat. That might prove expensive.

Hmm. I think the materials of the finish applied do make a difference. UV cured polyester, lacquer(s), oils (tru-oil) have different benefits. The UV cured polyester seems to stand up pretty well to sweat, lacquer and oils to a lesser degree. However, UV cured polyester is tough to repair. Oils are pretty easy to repair. One can also use wax on an oil finish to help reduce sweat effects.

Nothing protects a uke from temp, humidity extremes, except avoiding those.
However, I think the oils, as penetrating substance have less of a 'film' are thus less susceptable to cracking from temperature variations.
Just my observation, based on limited data.

I always thought the fun was in trying to wear it off...
Do know that all finishes but oil will "check" in temperature extremes (some just check with age...poor Martin). But you said crack. I am thinking you mean the wood itself, and nothing is going to stop that is you let your ukulele dry out.