Heroes 5.5 WarGame Edition - Tactical Edition.

no, they are a separate type of SpellSpawn; there are AttackeSpellSpawnDeath, etc. It is not possible to track the application of a specific spell, no.

unit turn (written for AI control, to be checked)

also under player control

spellcasting, application of any activated ability

it's not that simple with abilities; most require the creature to have the corresponding skill. Regarding spells: a hero can cast any spell available to them based on their skill in a school of magic (i.e., knowing the spell is not necessary; sufficient skill for casting is enough); creatures can cast anything, as long as they have enough mana, but it should be noted that this cast will always be at the Advanced level (unless the creature has a castable spell at a higher level). For example, for this reason, it will not be possible to create a phantom of a creature of level 7+ with a creature (but this is a rare, specific case).

It is possible to speed up or slow down the progress of unit turns (although they say they haven't figured out how the numerical parameter works)

from 0 to 1, 1 - send the unit to the beginning of the turn order, 0 - to the very end.

kill any stack

not exactly; the stack will be removed from the arena, leaving no corpse. However, it is still possible to emulate killing in a slightly different way.

It is possible to set/reset automatic control mode (for example, to emulate uncontrolled berserker turns in this way)

I don't remember exactly, but there seemed to be problems in this case (when switching to automatic turns with a script, it was not possible to switch back)