lady-bower Sometimes tar.gz files are static binary installations of a program, similar to how Windows programs work. However, tar.gz files can also be source code for an app, meaning you'll have to compile to get the app to work.
Usually extracting a static binary file results in a folder being created under a chosen location. I usually choose to install such files under /home/<username>/bin. Everything needed to run the program usually resides within the extracted folder/directory. You'd then need to figure out how to create a menu entry to the file that runs the program. I can't help with creating a menu entry unless you run the Openbox window manager, which I doubt you're doing.
I use the Chromium, Palemoon, Slimjet, and Tor browsers under Solus using tar.gz downloaded static binary files.
However, note what algent has stated. If the program resides within the Solus repository, you should use that.
Anti-virus: Well, if you're good at compiling under Solus, you could try compiling ClamAV and clamtk. You could also try searching for a Linux version of one of the major proprietary anti-virus programs and see if it might be installable under Solus. This post might be a good starting point to finding something.
However, as wingman-4 has stated, you technically don't need an anti-virus program on Linux.
Something to check for rootkits would be beneficial in my opinion. Debian has chkrootkit, a command line app, but that isn't available in the Solus repository.