It’s not a big deal adding fields to the registration form. It’s what to do with the provided information. The sort of checks you want to do will come from third party sites. These sites would need some sort of API to handle automated queries. Exactly how you would interface with their API would depend on the chosen site. It’s not something we are able to help you with here.
You can try searching for plugins that do all of this for you. The sites that offer the sort of information you seek might even have a WP plugin you can use. I am not aware of any such plugins myself. I’ll wager your search-fu is just as good if not better than mine ??
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