1. From http://fex.belwue.de/fex.html, it looks like the software can't be any older than 2006. Looking at the source, it uses things like rel="prefetch". The style is just an explicit aesthetic, then, like that of Craigslist.
2. Some of it could, yeah. Torrents make it easy to share files directly from your computer to a peer's. FEX solves a slightly different problem, though—the asynchronous "put the file somewhere, then let the peer get it while your computer is offline" use-case. It's somewhat cumbersome to use torrents for this (though possible: you and the server join the swarm, the server leeches from you, you leave the swarm, the peer joins the swarm, they leech from the server.) But, if you do use torrents that way, you won't [by default] get the "auto-deletion of the server's copy" property that FEX has.
(You could probably match 99% of FEX's functionality with a torrent client running on a server + a daemon running alongside it that can control the torrent client through RPC; but I don't know of any attempt to build such a thing.)
I use this software at work and can say that it is in active development (last version: 20180528 (Arch Linux)... that means just a couple of days ago).
But my favorite part of F*EX is the sharing of versioned file archives (https://fex.rus.uni-stuttgart.de/sharing/ ).
