Will my apps be removed from the App Store if my developer account expires?

Yes - all your apps will be removed from their respective App Stores if your developer program membership expires.

If your Apple Developer Program membership expires, you will still have access to iTunes Connect. However, your apps will no longer be available for download on the App Store and you will not be able to submit new apps or updates.

^{Source: https://developer.apple.com/support/appstore/itunes-connect/}

Attempting to log in to iTunes Connect will show the following message, but all of the services are still accessible.

Yes, your app will be deleted from the App Store until you renew your subscription.