My international game puzzle rating is shown with a question mark, while I've answered more than 3,000 puzzles. What's the reason for this question mark?

Puzzle ratings work the same as any other rating on lidraughts, so the question mark means your rating is provisional. Every glicko2 rating has a rating deviation that expresses its uncertainty, which usually decreases with every game/puzzle you finish (a rating deviation above 110 means provisional, causing higher fluctuations).

The rating deviation increases if you don't play games for a while, or when you play opponents that are much lower/higher rated than you are. In this case the cause must be your high puzzle rating. Beating many puzzles in a row with a much lower rating will slightly increase your deviation every time, up to the point where your rating becomes provisional again.