Chain trapping the skin: I think that with a thiner chain, the skin will be trapped more than with a wider chain, because there is more space were you can get trapped. That used to happen a lot to me, but not anymore... maybe is because I learn not to put the skin in that precise place, or something more

A good solution is to put silicon at the top of the tube, where the chain meets the tube, so there wont be any space where you can trap your skin.
Thumb spins: They can be done with almost any length, is just practice, so keep on.
Wrist rolls: Yes, when you change the length of the chain or cord, you have to change the way you do the technique,
Usually:
wristroll + long chain: you hold the nunchaku near the top
wristroll + short chain: you hold the nunchaku near the middle of the stick, so the stick act as a chain, and it moves in your arm/wrist.
With practice, and when you change often your nunchaku, this is a natural process, but for the first time, it may take some time to get use from long to short, or from short to long.
But remember, most of rolls have been done with almost all size of connectors, so is just practice till you get the results you want, but of course, it is easier with a specific length to do certain moves, so you will be more comfortable using long chain when doing wrist rolls.