1997 Peugeot 306 Peugeot 306 Stalling and other problems

Hi,

I have a Peugeot 306 XSi Petrol 2.0 litre 16V (R-reg 1997-1998

Here are my problems:-

1) The engine switches off now and again (stalls) whilst I am in neutral or driving in low gears (cornering in 2nd gear)

2) When driving at higher speeds on the motorway/highway, the gas pedal will all of a sudden stop responding. The engine is still on though.
Sometimes have to pull onto the hard shoulder as my speed is reduced so much, the engine usually finally kicks in and I can accelerate again.

3) The fuel gauge on reads wrong. I could start up knowing I have quarter of a tank and it will say I have half a tank of petrol.
I ran out of petrol when I was on the motorway and the gauge said I had quarter tank.

I have been told it could be the fuel pump and filter.

Any help before I go to the dealer would be appreciated.

Thanks,

Colin