Hello! I have 3 questions after my first play!
1)Stupid question. we are playing without the tactics cards. I have 3 cards on a stone (color-run) and my opponent 2 cards (let's say a 3 and a 7) there is no way he can beat me. Can I claim this tile?
Yes. The rules specifically say that if you can prove, using cards already face-up on the board, that your 3-card set is unbeatable then you can claim the stone. In your example, the color-run would beat anything your opponent would play anyway so you'd get the stone.
2)We are playing with tactics. If both have 3 cards on a tile do we have to wait until every possible tactic card that could change things on this tile (for example mud-fight or blind man's bluff) is played? Or does someone claim it immediately?
After playing down a card (but before drawing) you can claim stones. Tactic cards that alter the rules can only be played on unclaimed stones so even if there's a tactic card that could change the situation (like Blind Man's Bluff) as long as you meet the 3-cards-played-on-both-sides requirement then you're good!
3)Same as number 2 but I have 3 cards and my opponent 2. Do I have to wait until tactic cards that could change things are played? Or do I claim it based on clan cards only?
To be honest I'm less sure on this and the rulebook is not clear. It does say "no matter which card he plays next" so I personally would factor in possible tactic cards. I'm happy to be proven wrong though.