Even for online bill pay, checks are still very much a thing. Payments to big financial institutions, like credit card and mortgage payments, usually go electronically and are more or less instant. But not everyone is set up to receive electronic payments -- when I pay my property taxes or dentist using online bill pay, my bank just prints out and mails them a paper check, and it takes a week for them to receive it!

Yes, I only use a few of them a year. I bought a box of 500 of them back in 2006 or so and still have 2 unopened packages of them.

I pay my bills online but I've needed a check for things like government fees where they don't take credit cards (or charge a fee), paying the company who fixed my roof, etc. I've also gotten certified checks for things like a house downpayment.

Yes. Rent is usually paid via check, and they're still useful when interacting with some government agencies via the mail.