I'm Paul Phoenix
I play Gut Drill as a Reversal
If I use its Stun: 2, do I immediately Respond with Paul Phoenix, or does the opponent commit the 2 foundations THEN the Paul R goes through?

Obvious note: they are committing Torn Hero, which in turn will lead to them committing my Paul Phoenix.

You'd R first, as you've played the ability and are the active player.

With Paul you always play the Stun, then R to playing it. You need to choose what to commit before they choose what to commit for the stun.

If you are playing Paul, you should know what you plan to commit with him before you play the stun and so there should be little or no pause after declaring the stun until saying what you are committing with him.

EG "Stun 2, React with Paul and commit Card X. There it is."

Wow Shinji, important templating here that you aren't aware of or something? Not meaning to belittle here, just surprised.

Effects like Paul Phoenix's that respond to an ability "being played" respond after costs are paid, but before effects resolve. Stun is a keyworded Enhance with no costs, so you declare the Stun and, thus, the Enhance is "played" and Paul responds right away.

It doesn't hurt to be absolutely certain.

Of course, they can discard a momentum and throw Torn Hero in the way of Paul's effect, forcing you to commit Torn Hero instead of something else you wanted to target. Then they'd still have to commit two foundations.