I just got a quest for the Companions, to kill the 'leader' of Dimhollow Crypt... which is also the place where Serana is locked up. If I do this now, without having started the Dawnguard questline, can I start Dawnguard later on without getting in trouble because I already cleared Dimhollow Crypt?

Only the first area is unlocked. the rest of it is blocked by a rock.
You can do that companions quest without anything bad happening in Dawnguard.

Ah good thanks!

Ok, so I went to Dimhollow Crypt, and found only wolves, not the draugr I was supposed to kill. So I checked the map marker and it said I had to go into Dimhollow Cavern. So I went there, but couldn't go any further because it's the end of the dungeon and the lever to open the gate was on the other side of the gate. Can I go back to Farkas and say 'yo dude, you gave me an impossible quest, I'm not doing it,' or should I complete the quest with console commands?

Dimhollow Crypt should not have been offerred as a location for a radiant quest in the first place, because it is marked as "reserved" and also does not respawn. It would be best to revert to a save prior to getting this quest from Farkas, because you cannot quit the quest and attempting to complete it with console commands has a high risk of causing problems in further "Companions" quests.

Also, you may want to check to make sure that you are not using any mods that would conflict with the "Companions" quests or the radiant quest system (in general), because this shouldn't have been possible under normal circumstances.