one of my favorite cards...

Questioned Claim
Any phase: Each player that does not control a King or Queen character must choose a challenge type. Until the end of the phase,that player may only initiate challenges of that type.

If someone trait changes a character after the event has resolved, do they get to initiate more then one type of challenge? Is the event a static effect or is it a one time effect when checking for Kings and Queens?

Yes it checks at the time of the event and then doesn't check again. What happens is it sets up a lasting effect for everyone that doesn't have a king or queen at the time of the event. So if you get a king or queen later, it doesn't make the lasting effect go away.

What would happen if I played 2 of these in the same phase, assuming no player had a King or Queen?

Slothgodfather said:

Otherwise, the effect of the first will stop them from doing challenges of the type chosen for #2, and the second will stop them from doing challenges of the type chosen for #1.