How do I know if my iPhone is registered?

No idea. iPhones don't need to registered to be used.

Who said its not registered? Again, registered to what?

Your service provider should be able to give you a sim card you can insert into the iPhone to get mobile service.

Not sure what that website is, or is supposed to be telling you. Or what they mean by "temporarily available for use". You would need to contact the Website you are using for an explanation of their terms. That is not a phrase used by Apple.

Do note however, third party websites have no way of knowing anything about an iPhone from an IMEI number, so I would not trust whatever that website is saying.

There is no registration process for iPhones.

Check your Apple warranty status. Enter a serial number to review your eligibility for support and extended coverage.

Check your device's coverage

What do you mean by "registered"?

Registered to what?