1. Yes they still accumulate debt.
This is how I see it: A carpenter owes you a favour, so you ask him/her to renovate your bathroom.
That is the equivalent of taking a compel to do a mission for your sponsor.
During the renovation, the carpenter uses your tools. They eat the food out of your fridge and they use your car to go get supplies. These are all things above and beyond what a contractor would do for a renovation.
You've hired them for their expertise and they usually use their own resources(tools) and expertise to finish a job. But, if they ask you to cover their lunches the entire time, they're going to owe you.
2. If you compel a player to do something, and it fits the sponsor, I think it's legal to have the player say "I don't want a fp. I want it to go towards my debt."
In the same vein, if you allow self-compels, I see no reason why they can't self-compel and, instead of receiving a fp, have that compel pay off debt.