Jumps when Idle/Fuel level Sensor issue

[Hubcaps]

My car jumps when it is idle and jerks forward and all it gives me is a P0464 fuel level sensor circuit intermittent as the problem when I hook it up to the computer.

Could the fuel level sensor be the reason why it is jumping like that or is there probably another problem?

PS- Here are the services I have gotten so far in the past 2 weeks because of these codes [P0304, P0171, P0420]:1) Tune-up (caps/plugs/wires/fuel filter/rotot)2) changed both O2 sensors3) replaced valve cover gasket4) Fuel injector cleaner