#activated ability

Usually no.

When Mirage Mirror’s activated ability resolves, it becomes a copy of the targeted permanent without any modifications. It doesn’t retain its activated ability and as such won’t have that ability to activate again for this turn.

The only time you can copy more than one thing in a turn is if you activate the ability again in response to the first activation. The usefulness of doing this is limited, but can result in some fun scenarios.

For example, if you activate Mirage Mirror targeting Rampaging Hippo, then activate it again targeting Frilled Sandwalla and allow that activation to resolve, you can then activate Mirror/Sandwalla’s 1G ability to give it +2/+2 until end of turn, then let the first copy effect turn Mirage Mirror into a Rampaging Hippo with the +2/+2 from Frilled Sandwalla’s ability still buffing it.

Yes, it gains abilities that are granted to the creature, but not all auras grant abilities to the creature.

For example, Freed from the Real doesn’t grant any ability to the creature its on. It has the abilities that tap or untap the creature, not the creature. Kraj won’t gain these abilities. Oracle’s Insight, on the other hand, grants an activated ability to the enchanted creature and so Kraj will be able to gain the “T: Scry 1, then draw a card.” ability.

No.