I initiate an Power challenge with Khal Drogo.

I kneel Dothraki Handmaiden to increase Khal Drogo's STR by +2

After I win the challenge, I want to trigger Khal Drogo's ability to kill a character.

At this moment, is the +2 STR still exists? (Since the card says it's only until end of the challenge.)

What is the max. STR of the character I could kill?

Tks a lot.

The STR boost is present for the complete resolution of the challenge, including passive effects and responses. It's still there when you trigger the Khal.