I have a reg cab 4.6l f150 coding p0171 (bank 1 too lean) and p0304(misfire on cylinder 4). Being the truck is backfiring at the bottom of gears (its a standard), and stuttering in the gear and up hills, I was thinking fuel pump or clogged fuel filter. Any thoughts? I want to make sure I get it right the first time being its winter in the north, so any advice is welcome!

 

You may have 2 problems, but probably not the fuel pump.
You can get a fuel pressure tester for under $20 at Harbor Freight.
Check all the vacuum lines for a leak, crack, soft spot, particularly the PCV line which might be your P0171 code.
For the P0304 misfire on #4 pull the COP off and see if there is any moisture in there and inspect the boot which may be degraded.
If everything looks good try swapping the COP with #3 and see if the misfire moves to #3.
You may just need a new boot/spring.
Not sure if they're the correct parts, but the Denso 671-0001 boot/springs are $30/set of 10 on ebay which would give you 2 spares.
I've read that Denso is the supplier for Ford COPs.

 

Disregard the 171 for now. No COP's on that engine so no worries there.

You have a dead hole cylinder 4, disconnect the injector pronto in order to save your cats. Check spark on that cylinder first. That will point you in which direction to troubleshoot next.

TIP, - Use the starter relay when checking spark....short cut.

 

According to BR2011s profile she has a 2006 Ford F150 STX 4.6L.
I think that engine still uses the DG508 COP.

 

An 06? Huh, thought it was a 97 for some reason earlier. Replying to two at once no doubt.

Regardless, he's in the wrong forum on this site. br2011, -ask moderator Martian to move your thread to the proper forum to get specific answers for your ride. PM him here, -

https://www.f150forum.com/members/martian-139927/