And one more... we with my friend in multiplayer did all quests implemented in new patch, main and side. And now in singleplayer they aren't saved... I need to do all them again...
You have the reward for the quest already, the only thing you miss is having it done in your personal quest log. This is in case you want to start and finish the quests yourself, I believe.
If you joined into a friend's game and they turned in a quest they had already satisfied the objective for with you in tow, I imagine you'd be a little miffed over having content taken away from you. You lose nothing but not having it finished on your personal world save.