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For an extreme amount of white smoke with coolant loss you need to have the EGR cooler pressure tested, Odds are its cracked and dumping coolant into the intake.
You must resolve that prior to your contribution codes because alot of coolant can cause a misfire and mimic a contribution code. The codes you have normally just point to have faulty injectors which is very common on the 6.0. So you need to test the FICM and verify its not a signal issue to the injectors prior to replacing them. That test can download from Ford HERE.
Your overheating issue is most likely due to the coolant level lowering or a sticking thermostat but if your white smoke is minimal then you need to do compression and pressure test to check the head gaskets, another common 6/0 issue.