So I am playing this amazing game (kudos!), and I have a question that I can't interpret (I am Greek) about what happens when you lose a battle, either with an adventure card or with another character.

For an example, I draw an adventure card, and I get Dragon encounter. I don't have a lot of strength so I lose a life. What happens in the next turn? Do I have to leave the square or I have to keep fighting the encounter until I lose all lives or the encounter is defeated?

Do the same rules apply on encountering an enemy player? I can't seem to find anything on the rulebook, after the "you lose a life" part.

Aside from certain exceptions, you only encounter enemies or other characters on a space when you land on that space. So after you have a combat with a dragon/character and end your turn, you would not re-encounter them in the same space next turn since you will not have landed on that space again. You take your normal move, and encounter whatever is present in the new space you land on.

Some exceptions to this I know of are:

The Wildlander follower allows you to re-encounter a space you are in instead of taking your normal movement, if you so choose.

If you roll a 1-3 in the Mountain Pass space (part of the Highlands expansion), you must encounter that space (and any cards in it) again instead of moving that turn.

Hope that clarifies things!