Am I able to pay my monthly Apple bill by check instead of withdrawal from bank?

For digital products and services, payable through your Apple ID account, these are the possible valid payment methods:

Payment methods that you can use with your Apple ID (by country) - Apple Support

That does not include checks.

Not that I know of; but you may want to check with Apple just to be sure.

What monthly bill are you talking about? A subscription to an app, AppleCare+, or are you referring to the Apple credit Card?