You cannot save during battles, the engine does not support battlefield saves. The game does pretty well with paused battles, I usually don't have any problems stretching a battle out over several hours with interruptions. The VI expansion added the pre-battle campaign save, which is sometimes unreliable.
Generals are tied to their units, and units cannot be retrained to another type. The only changes that can occur are battle/siege unmounting of some units and royal bodyguard upgrades at the era changes.
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