I haven't the slightest idea.  You'd have to ask someone with that particular bank.  However, I think you know as well as I do that this is not what's happening and that the company is making the applications online.

I suspect that, if a credit card issuer knew what was happening, it might not allow it.  However, that's neither here nor there.  You authorized this company in writing to do what it did and therefore have no basis to object to paying the fee that you agreed to pay.  Moreover, if you objected to paying the credit card bills on the basis that the company didn't have proper authorization, you'd lose because you gave written authorization.  That the written authorization might not be a power-of-attorney is neither here nor there.

I said it's possible that a UT small claims court wouldn't have jurisdiction over a non-resident.  It is the case in many states that small claims courts' jurisdiction is more limited than regular courts.  I haven't looked up the rules to know for sure.

Yes.

I'll bet $5 that the contract you signed provides that, in the event of litigation arising out of the contract, the loser will have to pay the winner's attorneys' fees.