What does Eagle Eye give? Is it possible to use it to learn 5th level spells from the enemy? Can you learn Dimension Door and Town Portal this way?

Eagle Eye allows you to learn only combat spells. DD and TP are spatial spells, so Eagle Eye does not apply to them.

How exactly do you determine how many rounds the enemy will be stuck under Blind? I looked at the formula, but I don't understand it. Say the Hero's Spell Power is 5 or 10, how long will he be idle?

if you cast the spell, it depends on the amount of Spell Power + artifacts that increase spell duration; if Unicorns or Basilisks cast it, it's 3 rounds. So if your Spell Power is 2 and you have no artifacts that increase spell duration, then Blind or Haste, Slow, etc. will last 2 rounds, and if your Spell Power is 99, then accordingly 99 rounds.