Based on both of the points you said, I believe The following:
For the second point only:
Many NAS Devices with built in BitTorrent Clients work, but, are not very good. It is possible that it does not support DHT and the tracker you are connecting to is either offline or the file does not have any peers.
Your NAS either does not support UPnP, or you have UPnP disabled on your router, or you have not set up your firewall ports correctly.
The trackers you are connecting to are private and/or have some kind of status that they are returning but your client is not showing the message (e.g. wait time).
However when I also consider the first point combined with the second:
I believe that your NAS does not have an active internet connection. If you do not have DHCP active on it, make sure it's gateway and DNS are set correctly.
This would explain why it can not download/access .Torrent files via URL but you can put them there from your LAN, however, they do not progress at all.
I think I have covered all the possible reasons, I believe the last paragraph is the real reason, but, unless your NAS has a command prompt or any way to ping a site, I am not sure how you can test.
All this being said, if you turn your machine(s) off at night and just want the NAS to be a low powered Torrent client, fair enough - however, I have to say that a full torrent client such as Utorrent will give you a much better experience.
Best Answer
Torrents work by trading a few extra bytes downloaded and some extra software complexity, CPU time, upload bandwidth, and additional active sessions in exchange for the potential to download the desired bytes at a much faster rate.
So it depends on how you define efficiency. If your primary concern is for transmission size, then torrents are not efficient. If your concern is how fast you get your data, they are great.
Each of the costs I listed in my first sentence are real. They are designed to not be a factor for most users, but any of them can be important in the wrong situation. For example, the small college where I'm network admin has a fixed limit on the number of simultaneous sessions we can push through our gateway at one time. BitTorrent users can generate in excess of a thousand sessions each. Just a few users like that and suddenly internet access suffers for everyone even though we have bandwidth to spare, because we can't process more sessions.