1----
You can get a DVD with all the official packages here: http://mirror.switch.ch/ftp/mirror/slitaz/iso/3.0/packages-3.0.iso
It weights less than 2 GB. You can get it in an on-line computer and dump its packages in your own machine. Then, use Tazpkg as totoetsasoeur explains. Having the whole repository in your house is the best long-term solution, even for users with Internet connectivity.
2-----
There are lots of guides arround. The method you have to follow depends on the bootloader you have or want to use.
3-----
You can install Avast, but it needs some kernel variable hacking and you don't want to try that if you are not able to set a triple boot system :-)
In GNU/Linux, I recomend ClamAV. It is free-software, it uses to integrate well with Linux and does not drain your sources heavily. The bad news is that it has not very hight detection ratios against some specific concealed viruses. However, even with this issue, is a better solution than avast, AVG or other propietary stuff you may find.