Hey FBinNY, a quick update: I think I've solved most of the problems. I've managed to play with the barrel adjuster near the shifter, and I got the front derailleur tuned fine I've also greased the chain and let the grease spread thru all cogs, so now it's considerably quieter. Also the thumb shifting is not so hard anymore, so I can live with it (I guess Sora is Sora...).
I guess the only problem left is that some of the smaller cogs in the rear derailleur sometimes pick a chain link from the side, lifting it a little bit and producing some irregularities in the motion. Do you think some cog teeth might be bent? I crashed once but nothing bad.
Anyway, thanks for the help!