I have two questions regarding khums. If one is in dept, is it obligatory upon them to pay Khums? And who do I directly give my khums to for them to distribute it out?

Firstly you need to clear all the debts you have.
Once you have cleared them out, you can keep a calendar for your annual khums date and give the 20% of your annual savings towards the sehme imam and sehme sadat through the wakil of your marja that you follow.

I have two questions regarding khums. If one is in dept, is it obligatory upon them to pay Khums? And who do I directly give my khums to for them to distribute it out?

Depends on the kind of debt. If it is a long term debt (like a student loan, mortgage etc) then khums is wajib on whatever you have remaining after all your expenses at the end of the year.

If it’s a short term loan like day to day then you wouldn’t pay khums.

In case you have to pay, 20% of your savings of which half goes to needy and poor Sadaat whom you can give it to yourself if you choose, the other half goes to your mujtahid or his representative. The Sadaat portion can also go to your mujtahid who would distribute it accordingly.