Yes you can simply delete a program when you are done with it but check to see if you have a packager manager first. Redhat uses rpm which will uninstall many programs for you.
A tar (.tar) file simply takes a group of files and makes it into a single file for storage. A .gz file is what actually does the compression. So a tar.gz file is a file or group of files that have been grouped together into a single file and then compressed.
To install software like this all you have to do is..
tar xvzf FILENAME.TAR.GZ
and it will decompress the file into it origianl contents. All you have to do after that is go into the directory that it created and look for a file called README or INSTALL. Usually you will find directions int here about what to do next.
No you don't always have to install programs as root, but it is usually the case. You should find directions regarding that when decompress the .tar.gz file.