As Mazda said, the 443 is related to the circuit for the evap purge valve. The purge valve is the one on the intake. It is a circuit fault code, so it means there is an open wire somewhere. That somewhere could be in the valve itself.
Generally the test for this code is to place a small light bulb in the circuit, in place of the valve, and then command the valve on, see if the bulb lights up. I'm guessing you don't have a scanner that does active commands though, so I'd start by resistance testing the valve. It is on the line between the carbon canister and the intake, kind of a cylinder looking thing.
P0401, insufficient EGR flow detected. 90% of the time this code means the DPFE sensor has failed. It is a fairly sensitive unit that live in a very harsh environment. It's bolted to the intake near the EGR valve.
The P0420 is catalyst efficiency below threshold, bank 1. This is always a bad cat.
Since you have no check engine light, and all of those codes would cause a light, first I'd make sure the light works. If it comes on when you turn the key to run, the light works. If it does, I'd clear those codes and see if something comes back before going forward.