I know if a Hand of the King is attacked, it counts its STR during the challenge. My question is whether or not the Hand's text box can is also considered and used. For example, if my Hand is the core set Catelyn Stark, can I still trigger her character ability to blank an attacker's STR? Or if my Hand is Jaime from King's Landing, can I trigger his response if I win the challenge? Do the Hand's keywords still used such as Deadly?

Depends on what the actual ability says.

The Hand of the King becomes a participating (defending) character without actually being declared. If an ability on the Hand requires it to be a participating character, you're set. If it requires the Hand to be declared, you don't meet the play restrictions.

ktom said:

So a Hand of the King challenge would let you have 2 defenders when Desolate Passage is the plot since the hand is not declared as a defender. Right?