Quest is simply not working for me anymore, I've been into 2 out of 3 caves or whatever, and the third one says I need a key to enter, but there is no key, and arrow is simply standing above the gate...

Any help would be appreciated.

Which caves have you done? There is saarthal, germunds hall and folgunther. Take a look at the videos I have I did them, hope its helpful to you.

You need to start the college of winterhold questline to enter one of the caves (saarthal i belive).