Any idea why my fuel gauge needle goes up and down? mostly down of course
 

it failed long time ago and I never had a chance to fix it. Usually when I put full tank of fuel it goes up and stays there for some time and then goes down and then sometimes up again. It is very intermittent. What is it? What are the costs involved to fix?

fuel level sensor it sounds like
 

its probably shorting out or just crapping out.
depending on car its going to be of course attached to the fuel pump which might have to be pulled to be replaced.

I just recently replaced parts of my cluster for this.
 

My new, actually used, cluster seemed to fix the problem. I think, for me at least, there was some short in the panel or even the gauge itself that this would happen to me.

My fuel gauge, when full, would go all the way to F. Then sometimes it would drop almost to E, then go back up like to 1/4 tank. Very intermittent readings.

I suggest finding a cluster, pluging it in and diagnosing it that way. If the new/used cluster gives solid reading...then you knwo its not the fuel tank sensor, to which I think is kinda hard and difficult to repair or replace.

The sender is quite easy, comes out before you do a fuel pump on a B4.
 

If you have factory tools for doing the fuel pump, it'll help speed up the process, but not necessary IIRC.