[Injuneer]

EGR won't affect the way the car runs, as long as the valve isn't leaking. Removing it isn't going to affect the way it runs either, particularly start and idle, since it isn't used at startup or idle. But if the EGR is still there, and the EGR valve is leaking, it can cause misfires. If it was causing misfires, it would more likely cause P0300 - random misfires.

P0405 is basically checking the electrical continuity of the EGR position feedback sensor. Could be a problem with the wiring to the valve or in the pintle position sensor on the valve. If you had an EGR leak, it would more likely cause other EGR codes to show up, so I don't think the P0405 and the P0303 are necessarily related.

As noted above, anything that affects Cyl #3 is suspect. If you've ruled out the plug and wire, as noted above there's still the coil and the injector. And it could also be a valve problem... e.g. lifter.