My number tab is not showing any number and it's blank. I am unable to tap on it to input the number myself. Hence, iMessage and Facetime can not be accessed using my phone number.
How can I get my iPhone to re-read my SIM card or cellular service so that it shows in the settings app and I can try again to set up messaging using my proper cellular number to combine with my AppleID/iCloud account?
I can’t reproduce this, but here is how I would troubleshoot it and why:
At this point, you can be sure the SIM isn’t trivially failing and the iOS had a chance to talk to the cellular carriers. At this point, I would back up the device and then erase all content and settings. Now make a tea or coffee and get ready to call/engage tech support for your cellular carrier and explain you’re needing help knowing why your device isn’t working with their service. They can’t really say there’s a bug with iOS or your apps if you’re willing to repeat the reset network settings / power cycle / erase all content and settings. They might say - check with Apple and Apple would say, restore the device and if it still doesn’t work go back to the carrier.
At that point, the carrier is really on the hook for providing you a reason why your service isn’t working. Similarly, Apple support will be a breeze to erase / restore / rule out trivial failures and fix this in almost all cases without waiting hours on either call.