Hello, first of all I shall direct you to the Rules Question thread, which is better suited to general questions.
Now, to answer your questions:
- What does it affect? Your opponent’s units, and your units (but in two different ways).
- Only unit attacks are blocked by Moment’s Peace. Unit abilities can still be used just fine, and Heroes can attack as usual.
- Note that your opponent’s units cannot attack, and your units cannot patrol. Heroes can attack and patrol as they please for both players.