Linux has different ways to install software, unlike other platforms in which you just click on the next buttom. It adds a level of security so malicious software wont take over your computer.
The first thing you need to do is find out what is the administrator password so you can install the browser you need.
Perhaps the person from whom you bought the computer would help you with that.
Once you have the password you can install Adobe Flash payer which is what these games and videos in facebook requires.
In Linux there are always two accounts one is the regular user who log in the computer for everyday things without having to change anything in the system
And the aministrator or root user who does changes in the software, install new software and changes settings and other stuff.
The password for your regular user can be the same as the root user depend on how the operating system was set up from the beginning.
I am assuming you are using fedora as your linux distribution?