So, if there is no battle at the first planet due to lack of interest it is removed from play before going on to the next round. This means a game last max 7 rounds, right?

What happens if no one has 3 planets with 3 matching symbols? Who wins?

This is covered in the game rules. In the event that no-one manages to claim three planets with matching symbols, or a Warlord kill, then victory goes to the player who most recently added a planet to their victory display. If a game ends with no planets being claimed by either player (incredibly rare but not impossible) the game ends in a draw.

Thanks for clarifying. Didn't find it in the rules but will dig deeper

It's under the entry, "Winning the Game" on p. 16 of the RRG.