I never was so teed off in my life when all I could put in my 88 Supra was ethanol gas, had to redo the entire fuel system. Only sign by the gas cap cover was do not use leaded gas, like you could even buy leaded gas in 1988. Ethanol must have been around back then because my 1986 boat has a big sign by the gas cap, do not use ethanol.
So whats the story on your 2001?
With a rough running engine, first step for me is to do a compression test just to get this out of the way, then the ignition using a spark gap tester on each cylinder, if applicable, ignition timing, then check for vacuum leaks, fuel system comes last.
In particular with EGR problems, if compression is low, verify this with a cylinder leak down test. Then flip a coin to determine whether the vehicle is worth repairing or not. On heads that I have pulled either a crack in the head or nothing left of an exhaust valve seat. But don't go this far, even before throwing a cent at it. Son's 2000 Taurus was this way with a cylinder down to zero with 256K on it, and a DOHC engine at that. Just drove it to the wrecking yard and got 300 bucks for it.