You can dual boot with windows, without having to remove it, but you have to make sure that you partition a section that is big enough for Linux, to be safe at least 10 gigs.
Now, if Linux free, yes and no.
Linux itself is Free as in Freedom, not Free as in Beer. What this means is that you can always look/edit/use Linux code for whatever you want, it is all opensource. However not all Linux builds are free. They are all cheaper then Windows, and there are some that are free.
Ubunto is one build of Linux, that is free to use. It has been gaining popularity because of its ease of use. However, it does require some decent specs on your computer to use it to its best ability, your computer is a bit old, and it might be very slow. There are other free builds of Linux that are not as graphic intensive, and would run a lot better on your PC.
Linspire, is a version of linux that is not free, but it is pretty cheap, and its based to look and work like windows.
http://en.wikipedia.org/wiki/Comparison_of_Linux_distributions - This is pretty comprehensive list of linux distributions.