Equip only to a Gotham Knights character.

Equipped character can attack as though it had flight and range and has "Activate >>> Negate target payment power effect."

Can Utility negate powers like Garth?

Can it negate powers like Terra or Roy Harper?

Any power that uses the -> arrow is a payment power; all of those you've mentioned use the arrow, and so all are payment powers, and so Utility Belt can negate any of their effects.

Remember that costs (pre-arrow) were still paid for negated effects, but the entire effect (post-arrow) is negated. If you negate Roy Harper's effect, your opponent still had to KO a resource; if you negate Terra's effect, no location is KOed.