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RE
On writing something on the back of the check, that's a restrictive endorsement. State laws and caselaw vary a LOT, but by and large it's not a useful exercise. I've read a lot of B.S. stories online about REs, but by and large I find these stories to be B.S. and there's nothing credible one can find to support them.
If writing "paid in full" on a check fulfills a debt, then I'd write it on the back of my mortgage payment and the house would be mine, free and clear. Obviously, that ain't gonna fly.
However, even if you live in a state where REs are rock solid under law, the payee can electronically submit the check, and your RE won't matter--unless the check is drawn on a bank or CU that uses routing numbers on their checks which cannot be submitted electronically. It's not commonplace, but it's out there.
AFNI
On the AFNI collection, if you know with certainty it was CO in 2001, then FL SOL is either 4 or 5 years, and either way you are out from under the SOL on it. If you aren't sure, then odds are probably good it is still under SOL--Murphy's Law and all.
Some people are very skittish about DVing a CA out of fear it will evolve a lawsuit. Me personally, I have a sh*t or get off the pot attitude. I'd rather know, one way or another. If the collection is bogus, and the CA knows it, then DVing them will make 'em go away because they know they don't really own the debt. OCs are notorious for selling and reselling debts to different CAs in effort to get it collected. AFNI might at one time have legitimately held it, but no more. Only way to find out is to DV them.
Car Loan
Do you currently have a car loan, and is it with the same company reporting the lates?