Hi,
Had a similar problem with my MkII GTi found it was the tank fuel pump, this is in the boot, right hand side held in by a circular plate. What I can remember cost about £25 from GSF. fairly easy to fit, be aware of the fuel fume when you do it!! As far as the fuel gauge. sticky float arm or possible wire broken on the wiper coil?
Cheers Terry
Should have said it's called a 'tank lift pump'