First of all, welcome. I hope you can find your answers here.
While I'm not that experienced myself, I do have some suggestions that *may* help you.
What programs are you trying to run specifically? Have you checked your hardware against the hardware compatibility list available for mandriva? If not, check here: http://wwwnew.mandriva.com/en/hardware
If you're trying to install a program, make sure you have all the requirements for that program. Whether you're using packages to install, or compiling direct from the source, check that you have all dependencies for that program (some programs require other programs to operate correctly)
As for tar.gz files, it's relatively simple. Just do the following in your terminal command line:
tar -xf packed_files.tar
That should get the files out of there.
Lastly, the line/webs problem sounds like a driver problem. Check that the driver used matches the model of your monitor. You should have a GUI configuration tool that allows you to choose your monitor's make and model. Check your refresh rates and resolution. If you don't know what the highest you can use for your refresh rate and resolution is, I recommend using 60Hz refresh and 1024 x 768 resolution. These settings usually will work with %99 of the monitors out there.
Hope that helps you. Might not though, I have limited experience. Good luck.