Lots of things I see wrong here...
First: its stock head bolts (not studs, there is a difference
Second: you need a monitor and if you were told the oil cooler was plugged (ECT 190 EOT 225 which is several plugged) why did you choose to drive the vehicle anyway? The many reason a egr cooler goes out is because of the oil cooler being plugged... Guess what comes next, head gaskets. (Probably not your issue though).
Third: just flushing will only plug the oil cooler more, especially if you use chemicals like restore, restore plus, vc-9... So you HAVE to replace the oil cooler, I'd do it immediately. A month ago your deltas where 35* and without a monitor there is a chance they are getting worse.
Fourth: the buzzing noise you hear when you first turn the key on is normal. It's the spool valves inside the injectors helping with cold starts (stretching their legs, warming up). Haven't heard a louder than normal fuel pump... So not sure there.
Fifth: get he FICM fixed and then see how the truck is acting and if it's still smoking... Hard to diagnose something truly without fixing all known problems first!
Sixth: the egr code is probably the egr valve gummed up and stuck in place not allowing it to open and close properly. Most times it can be pulled out and just cleaned... Don't forget new o-rings
Seventh: have your fuel pressure checked. It could just need a new spring which most guys get the updated blue spring. Fuel pressure should be at least 50-65 psi.
Eighth, last but not least the biggest issue you have!: since you don't monitor or fix known problems as soon as they are brought to your attention (could be lack of money
) a 6.0 powerstroke is not for you. Unless you like fixing problems that could have been avoided in the first place. Not trying to be a jerk... 6.0's are picky and require regular maintainence and monitoring of engine vitals regularly as well. Good luck with the truck.