The fuel pump on the Gen 9 Corolla rarely goes bad. It's well known to be a very durable item on this application. 352K miles on my original fuel pump. P0118 is often the temperature sensor (you've already replaced it), but it could also be the wiring to the temp sensor. It could also be very bad, dirty, or rusty radiator coolant.
Your car thinks the engine is always hot, even when it isn't, which may be why it's hard to start when it's cold and why the fans are on. A faulty A/C pressure switch could cause the fans to run at high speed even if the engine is cold.
I had no signal going to my front O2 sensor. The wiring was undisturbed, but I eventually found out that a shielded wire had the outermost wire penetrate and short out the signal wire even though it looked undisturbed. Does the coolant temp sensor have a wire that is shielded or a wire that eventually turns into a shielded wire downstream of it?
Yes, I think that's a good idea to check for 5 volts at the connecter, and jumper the connector to see if max temp is registered at the ecu as displayed on a scanner.
