2005 superduty- 6.0 Started ideling rough all of

i have seen many strange things happen with the distrib cabs on these

Ckeck your govenator .

has a breather pipe come off ?? this will cause the exact symptoms you describe

draw a small amount of fuel about 1 quart in sutable container and let sit then check for water.It will seperate in the sutable container

Check make sure all plugs are firing. Sounds like what my 93 Rodeo was doing-Idled okay but very rough when in gear. Turns out only 5 out of 6 plugs were firing due to a defective ignition module- 100 bucks later it works fine.

Hope this helps.

test for spark at the 2 plugs

well the question is where did the coolant go. if it didnt leak out it must have went out the pipe. As you stated, white smoke, white smoke is coolant. You definately need to get this to the shop. You cannot drive it this way or further damage will occur.

Sounds like an ECU issue.  check your fuses, see if you can get an error code from a scanner, they have one at most checker auto stores that you can use for free.  Could be a Intake Air Temp sensor or a Throttle Position Sensor.  Thats what I would start with.  Good luck.

bad injector?
easy to test with vom, just check from terminal on injector to ground if one reads different thats the problem, you do need to disconnect wire to check, my help is free and will be glad to help further just vote fixa..LOL my rating is all I care about. Hope yu can help me too.