It also says “free of installer bundles” while (at least in past, don’t know about now) their default windows installer was including ads (source)
P.S.: If you want to disable the in-app ads, here’s how to: https://gist.github.com/yunooooo/87564a0293a1c7a53fb3e233a604c638
Why not use free download manager instead?
Does that one have something like Click’nLoad and a Browser add-on or app to allow for it when the Downloader is running on a remote machine? Can it run on my server and be accessed through a browser or said app?
Does it handle various hosters including debrid?
I’m not sure about Click’nLoad or Debrid, but aria2 does all the other things you just listed.
I do not know the answer to some of your questions, but it can handle download links directly from the browser