Engine Flameout:
You'll see ENG FAIL in the EGT box. There will be N1 and N2 rotation. FF, OIL PRESS, OIL TEMP and QTY will have some figures in it.
This doesn't require any memory action. (Key is to look at N1 and N2 rotation)
EEC Fault:
Again EGT box will read ENG FAIL, there will be N1 and N2 rotation or a value in the box.
All other values will be BLANK.
SEVERE DAMAGE :
You'll see ENG FAIL again, key is to look at N1 - THERE WILL BE NO N1 rotation.
N2 will still be rotating, all other boxes will have some value.
Memory actions initiated at 400'
Separation:
You'll see ENG FAIL in the EGT Box.
N1 and N2 will read 0.0 and all other indications will be BLANK.
Again initiate memory actions at 400'. Aircraft will be a tad bit more difficult to handle as compared to normal engine failure.
Now with SEPARATION: ENG1 - Degraded HYD A and ENG2 - LOSS OF HYD B.
I have a diagram of this explanation. Was unable to post it here. Best of luck with your TR.
Oh and I forgot to add further to your question:
ENG FAIL AT V1: PM calls ENG FAIL, PF calls CONTINUE, PM calls Rotate, Positive rate, PF asks for gear UP.
400' - HDG SEL - BANK ANGLE 15 degrees - IDENTIFY - INITATE MEMORY ACTIONS
Declare MAYDAY if time permits between 400' - 800'
800' - Fup SPD, retract flaps on schedule, FLAPS up, LVL CHG and select MCT (Max Cont Thrust) from the FMC.
DODAR!
Go to your EOP (Engine out point) or take off alternate and do the checklist for the non-normal condition followed by after t/o procedure and checklist.
Do a NITS briefing with your cabin supervisor. Nature/ Intentions/ Time/ Special requirements.
Decide where you're going and continue with DEFERRED Items checklists.
Thats all that I can think of. Hope I covered everything.