Unfortunately the "GET API" as you call it is integral to the functionality of NodeBB on the client-side. During the normal usage of NodeBB, it is constantly using the /api to load new pages, etc. It's not something that can be turned off, but it might be possible to restrict it to only accessible to users with a certain cookie. This doesn't currently exist, though.
You can open an issue on Github if you'd like this looked into further.
You seem to have installed either featured-topics-extended or featured-threads. Neither of these is included in the default package.
This appears to be a bug, since the option should not appear for non-moderators. However, the buttons do not actually work.
As for broken links, I tested my plugin featured-topics-extended and all links are working. The plugin featured-threads is broken however.
Damn I keep forgetting to turn on the "Watch topics you create" option so I keep missing replies on here. Sorry about that!
Thank you very much for the response, I just figured that out today actually. I had both installed still so I thought that all "featured topics" plugins were broken on my forums, after I disabled the other one yours worked.
P.S. (Not sure if it's a new feature but I didn't see it at first) But I love the featured topic cards. That's exactly what I was looking for when I first joined these support forums. Keep up the good work!
P.S.S. If you ever need any testing grounds or anything on a large scale for your plugins, our forums got almost 13,000 registered users in under two weeks and we expect it to continue to grow.