Really? It's pretty specific, and I don't think anything like it exists right now. You would need a device made specifically to download videos from numerous sources onto an fixed internal drive. It would also need to be able to transfer the videos to an internal removable drive (not sure what this means, possibly SD card or removable HDD?) and play them back, edit them, and do additional processing to them.
It doesn't sound like any Blu-Ray play I've ever seen. It's more like an Internet DVR device that also lets you edit videos and play them back on your TV from the device. That sounds pretty non-trivial to me.
One of the things you can do with BitTorrent clients is to have the client look for new torrents in specific locations (new episodes of a show for instance). The client with download the show to whatever location you specified, which could include a USB device if you so chose.