DISCUSSIONS on “Rules for online games in HoMM3 and formulas for calculating player rating.”

If, during a battle, a composite artifact belonging to the attacking player casts a spell, but the hero from the book itself does not cast a spell, does the attacking player have the right to bribe (flee) in the first round?

The attacking player does not have the right to bribe (flee). It is not the hero who casts the spell, but the player. It doesn't matter whether it's through a spellbook or cursed armor. Don't "humanize" the heroes; they don't do anything on their own.