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.

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!