Welcome to the forum!

1. EB maxes out the RTW engine, so you'll see the bugs in this engine come more often, that is nothing we can do about. Random crashes can be prevented by switching to the Alexander expansion, check out the unofficial-mod section in this forum.
2. For all technical problems while playing EB, the frequent issues are a good point to start. There are many reasons described why something goes wrong and there you can find workarounds too.
3. If you have a persistent crash that you can't solve by yourself using the advices given in the frequent issues, posting a save-game while give me the chance to load it on my build and see if I can get it to work.

Concerning your specific problems with battles:
Waiting at the result-screen for 15-20 seconds before returning to campaign-map minimizes the crash-rate.

XSamatan