1. You don't need point to download a torrent off DAT. To browse the torrents on DAT, just go to
http://www.datorrents.com, and browse or search for the torrent you want.
Every torrent site runs or has its own rules for who gets access to the torrents or who is allowed to download them, so I can only tell you DAT has no such rules, I can't tell you what applies to every site.
2. (and 3) .torrent files are files with data on how to download the files/movies/games you want, using the bittorrent protocol. At the very least, you'll need to install basic bittorrent to run torrent, but many use other bittorrent clients (such as Azureus, utorrent, bittornado) to run because they have a better graphical user interface and more options.