602.5e Activated abilities that read “Activate only as an instant” mean the player must follow the timing rules for casting an instant spell, though the ability isn't actually an instant. The player doesn't actually need to have an instant card that they could cast.

Can you activate abilities as an instant?

You can cast any number of sorceries, instants, creatures, artifacts, enchantments, and planeswalkers, and you can activate abilities. You can play a land during this phase, but remember that you can play only one land during your turn. Your opponent can cast instants and activate abilities.

Can you use abilities on opponent's turn?

Yep. If they have an ability that would do so, there is nothing stopping them (aside from Summoning Sickness, targeting, the usual). Unless you are playing with Area of Effect.