Simple answers to complex questions.

How do elves cast a spell on the hero's arrow?

It's simple: click "hero's arrow" in the book, and then the screen will show the spellbook again; choose the most lethal one or whatever you like, click it, and that's it. Nothing else happens this turn, but in subsequent turns, the hero simply shoots and a spell is cast along with the arrow. For example, if you chose ice block, you shoot—first the arrow hits, and then the block crushes them; mana is consumed during this process. It is profitable to use in prolonged battles. By the way, "wizard's mark" for mages seems to work similarly. You cast the mark on a unit, for example skeletons, then you hit liches and the skeletons take the same damage, or if you hit the skeletons, their losses are doubled.