I am not the Post office!

I am not the Post office. I am not a postal worker. I do not know where your bill is. I do not know where your mailed payment is. That being said;
Yes. You still have to pay if you have not received a bill.
No. A check in the mail does not count as a payment.
There are other ways of knowing that your payment is due.
There are other ways of making a payment.