@fffddd-dfeeedd No, most likely they will not affect Google rankings. Any external links from NodeBB are automatically nofollow'd, and those bugs you've pointed out don't affect ranking of the page itself.
@ningji that's been there for a long time now. You just need to have one of the search plugins installed and activated. nodebb-plugin-dbsearch gets installed by default. Activate the plugin and restart NodeBB to see the search icon.
@yariplus FYI... plugins themselves don't add that search menu. NodeBB checks for any active plugins listening for the hook filter:search.query to decide whether to show or hide the search icon.