Am I allowed to ask another player of how many cards he has in his hand at a moment of a game? What part of rules states it or otherwise?

Of course. It's part of the public knowledge of the game, similar to what he has in his discard, planets he's taken, etc.

There is nothing in the rules that specifically says, "The number of cards in a player's hand is information open to all players at all times." However, there are cards that refer to the number of cards in a player's hand (e.g., Ammo Depot, Inquisitor Caius Wroth), so that's a pretty clear indication that the rules don't allow you to hide the number of cards in your hand from your opponent - just the identity of those cards.

Thank you for your answers!