Does it 'stop' if you reach the quota or do you get a bill?

If you don't put in your credit card info, it stops. Otherwise you get a bill.

I don't have any personal experience, but as I understand it, that depends on whether you enabled billing.

Don't you have to provide a CC to sign up for even the free tier? (That's how it was when I was trying it out a couple of years back.) It was really cute too, Google would send me a $0.00 invoice each month.

I don't remember. I've been using it since the beginning and I don't get a bill.

I don't know how up to date this page is, but here's how it used to work: https://sites.google.com/site/gdevelopercodelabs/app-engine/...