The best way to test a fuel pump to make sure that power is getting to it is too get yourself and old car or truck horn... Yes i'm serious!
What you do is...
1) disconnect plug at fuel pump.
2) connect Horn to power via the small tab on the back of the horn using a 16 or so guage jumper wire with alligator clips.
3) there will be a threaded screw just sorta sticking outta the back of the horn that will be your ground, use another jumper wire to a good body ground.
4) last but not least turn the key on (run) and if your horn is connected correctly and there are no shorts or breaks in the fuel pump circuit... then it will honk.
depending on how loud the honk is you can judge whether or not enough power is getting to the pump...
which in most cases there is some corrosion on the ground terminal of the connecter (seen lots of em)
as for your fuel gauge it depends on what kind of sending unit was used but sounds to me like a short to ground or a but it could possible be that there is no ground at all it is just completley corroded off.
hope this helps