1..."is a little bit thicker than the original one. Is this a problem?"
How many millimeters thicker?......if 1mm not a problem...if 5mm could be problem.
2..."How can I check if it's ok? What kind of problem I can meet if I drive with a damaged one? Is there some warnings produced by a broken seal (I mean weird sound, high heat...)"
You can check quill seal three ways that I can think of.......1)remove the quill bolt, visually look at the seal inside timing cover, see if there are cuts, tears, rips, fragments of rubber (or cork seal if installed); 2) when inserting the quill bolt back into the rubber or cork seal, there should be a bit of drag on the bolt tube (if no drag or tube has lash from side to side, the seal is worn out); 3) check the oil flow at the head by opening the tappet door and see if there is good flow of oil dripping down from the head while engine running.
The reason being that if the quill seal is not sealing, the oil will not be at pressure into the crank. If no or little oil at the crank, there will be even less at the head (or tappet door).
3)"When I replaced the new copper whaser and screwed the quill bolt in his seat I felt some kind of resistance when screwing. Is this normal?
Yes...a small amount of drag is normal (however, if the drag feels like gravel between two pieces of metal, that is not good. The drag on quill bolt should be smooth like sticking your spoon into a block of jello, tofu, custard or pudding.