It's not possible to declare an attack against a minion here. If you attack an avatar here and a minion defends, the minion becomes a legal target, per the Defend rules.

Does this site protect minions from cards with the word 'attack' in their name, like Leap Attack or Spin Attack?

No. Dome of Osiros only prevents 'attacks' from the Move and Attack basic ability, or other card text that uses the word 'attack' (e.g. Crave Golem).