Do public bitcoin nodes have a public page to view node data? And if so can one add additional information to it? Do public bitcoin nodes have a public page to view public node data? Example is from monero public nodes: http://node.xmrbackb.one:28081/get_info -- it shows the node information.
Do Bitcoin public nodes have a public page that is accessible by the public? And if so, how can one add in additional values like for example a bitcoin address or an email address?
No, there is no such thing.
Bitcoin nodes in general only speak the P2P protocol with the public, not HTTP.