This is a great report and you found something real thank you for going to the trouble of editing it with your theory afterwards.
Your instinct was close. What's actually happening is that four things land in the same instant at month end: wages come in, cost of living goes out, and then the payment is taken. So the cash number never moves by the amount shown next to "Minimum payment" it moves by the net of all three. And when you can't cover the payment, the game doesn't take anything at all: the interest gets added to the principal instead, and you keep the wages. That's the "free money" you saw. It's doing what it was designed to do, but there's no receipt anywhere showing you that, so it just looks broken. That's a fair thing to call a bug.
It also has a nastier side you spotted without naming it: missing a payment pays you, which is a perverse incentive I need to fix.
On the credit rating you're right, and that's the bigger problem. It's meant to be the spine of the whole act (drop your rate from 10% to 1.5% and that's how the debt becomes payable), but the way it's currently balanced you finish before it ever becomes relevant. Same with the schemes: "Sell the car" and the rest are a permanent global multiplier on everything you earn, but all four of them unlock in the last 3 minutes of a 35-minute game, so they fly past in a blur. No wonder they felt like they did nothing.
Everything you listed is going on the fix list. Thanks for playing it properly and writing.