Generally, the way that Linux distributions handle software is quite different from the Windows way. Most distros (not all) have repositories where installation files designed for that distribution are kept. There are official repositories maintained by the distro and unofficial repositories maintained by third-parties.
In addition, you can download individual programs in the package format for your distro from some sites. For example, the Opera browser offers programs in *.deb (Debian format), *.rpm (Red Had format), and *.tar.gz (generic compressed file). You can also "compile from sources," which means you download the source code, usually in a *.tar.gz file, and instruct your system to compile it into installable format, then make an installable file, then install the program (the command sequence is usually
but sometimes ./configure is not needed.)
"No packages found" means that there are no packages in the software repositories in the software repository list on your computer.
A *.exe file would be a Windows executable. Windows executables will not run on Linux.
In most cases, there are Linux equivalents to Windows programs--Linux programs that to pretty much the same thing, such as GIMP for Photoshop or Paintshop Pro, Open Office or KOffice for MS Office, more media players than you can count, and so on.
In some cases, a Windows program may be so specialized that a comparable Linux equivalent doesn't exist; this applies primarily to highly complex and specialized programs with very narrow audiences, such as AutoCAD or medical records programs.
Many Windows programs can be made to run under WINE, a program that enables Windows system calls to be translated to Linux-ese and answered by Linux utilities and libraries.
Instead of using apt-get, I would suggest you start the Synaptic Package Manager. It has a GUI and a search function, plus an easy way to change the repository list through the GUI. You could enter "torrent" in the search window and it will list programs, libraries, and utilities related to torrents. You likely already have at least one torrent client included in your Debian installation.
My Debian Lenny came with the Transmission Bit Torrent Client--at least, I think it came with it, since I don't remember installing it.
Here's an earlier LQ thread about Debian repositories:
Linux is not hard, but it is different. There will be a learning curve, but it's worth it.