After jumping dead battery I'm getting a check engine electronics and the glow plug light is not going on before I start but staying on after the car is started.
Is there a series of actions that will reset it?
Or will it reset after I drive it a certain number of miles?

A conventional boost on cars with electronics for the car being boosted or the car boosting is always a risk. Usually you will get away with it but not always.

My policy is to jump on to another battery and let it charge up. Or if someone where boosting me to just let them charge my battery up. In both cases not trying to start the car before disconnecting the cables between them.

I have dealt with and seen some of the issues that arose from boosting when cars where much simpler with far fewer electronics long ago. No the booster cables where not put on backwards either.

I never was sure of why this occurred either but it did on occasion. In the old days it was simple things like cdi ignition components damaged. Sounds like you have a later model since you have an engine light. Find out what the codes are indicating.