Osom, part of the problem is focus. You are all over the place with problems. Start with one task and learn it then you can re-apply the knowledge to other tasks. Lets look at getting software.. I'm using Studio64 Linux (deb/Ubunto). It does not use RPM but the concepts are the same.
Getting software in Linux works in one of two ways.
In linux, you have registered repositories which are basically pre-compiled catalogs of software that are designed for your distribution. You can run the package manager (someone else chip in here because I havent used Mandriva since it was Mandrake) GUI that will allow you to search for software in the repository and it will install it for you.
When this doesn't work, usually because the software you want is new or not specific to the distro you can go to a website and download a file to install. However, at that moment, you might notice several different types of files to install. E.g. RPM is the best way for you, because then you can install and uninstall through the package manager or by using the URPMI program. It keeps track of the files just like windows installer does. A tar.gz file is a compressed file that uncompresses into individual files. But it is not registered with the system like a Windows installer. Instead it just puts files where they belong.
So, start with the program you want the most and see if you can use the Mandriva Package Manager (someone else chip i here, I'm rusty). Is it in there? If not, then go to the web site and get the RPM. If it's not available, look for the tar.gz.
Regarding playing of AVI, try downloading and installiing VLC Movie player. Very robust, gets codecs for you and shouldn't have any problem playing avi..