NF: I did not quote you at all, it was a disagreeable reply to your post.
KingAir1978:
1) The legalities are sorted the usual way, no need to modify anything. In case you got a start valve stuck, you try again and if unlucky then taxi back to get an engineer with a wrench, or take another decision. You are already in the flight phase.
Speaking of LEGALITIES, in case the same happened during convnetional Push-Back, you do NOT get to try one more time. It is a return to stand, Tech Log entry, and then MX. First movement under own power / dispatch phase and all ....
2) For tailpipe fire: In order to action the appropriate C/L you need to be told, true. But in a place where you'd actually perform an OEI t-out, there will be plenty of people to advise you of the fact.
3) Fuel leak during engine start - that's a good one! Unlike tailpipe fires, or start valve failures, this actually happens now and then. I assume you have this in mind
hhVl.png
(CFM engines)