Fuel pump and sending unit oddities

I don't actually know if its actually a problem.... but I thought I'd check.
2000 Chevy S-10 4.3 Vortec 6-cyl 100,000 miles
I just replaced my front two (one on the driver side one on the passenger) O2 sensors after getting a check engine light. When I turned the key to start my truck after that, like normal, my fuel pump did it's normal buzz for about 2 seconds, then was quiet. I started the truck and unlike normal the buzzing started and stayed on. Is this normal...? it never happened before... I didn't touch anything else except my o2 sensors, could I have done something there? The buzzing is defiantly coming from around the gas tank. I haven't noticed the truck running ruff or anything... it seems to drive fine.
Also the truck has, for about 4 months now, been inaccurately reading my fuel level. Most of the time it says full, and only goes down to 3/4 tank. When it's completely empty it will show near empty sometime. Could this have anything to do with the fuel pump, if that is what it is. And in any case could someone tell me how to fix it or what to look at?

I appreciate all help and input... thanks

If it is the fuel pump getting extra noise have a look at the fuel filter.
A plugged filter wiill overload a fuel pump.
MT

thanks for the tip... I'll check.
Any ideas on the sending unit? How easy are they to replace? Is it worth it if I'm going to sell the truck?

Fuel pump and fuel sensing uint are in the fuel pump module.

When you replace the fuel pump you get a new sending unit.
Kills two birds with one stone.
MT