For some strange reason my characters isn't getting any xp after finishing a mission/quest battle and they havn't reached max level yet even those that is still level 1 don't get any xp.

Do you receive crystals ?
When your fair-play status is bad (basically you have a small red triangle beside your pseudo in the room), you gain less crystal and less XP at the end of each game.
And less means you can receive 0XP and 0 Crystal.
To change your status, you have to play the games until the normal end (no quit, no time expiration) until you receive the standard reward.

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Collectionneur de cartes

I don't remember having any small red triangle beside my pseudo.

Does this also go for the adventure mode, because I have never experianced this before?

Yes, it does for the adventure mode also.
If you leave too often or let the game finish by time expiration, you have the same diminished rewards in room, tournament or adventure mode.

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Collectionneur de cartes