That's a problem with your website and the way you made it, not Firefox. Firefox adheres to specific standards; IE adheres to Microsoft's own standards, that just so happen to sometimes tie in with the official standards everyone else uses.
So, the code you used will be IE-only, and hence why it only worked in IE.
Yes, you can have many browsers on your computer at one time. The only exception is IE itself -- it's rooted into Windows itself, so without some hacks you can't run more than one version of IE at a time.
http://www.mozilla.com/firefox
It's free, so give it a whirl! I'd recommend you install Adblock Plus. It does the same job as Adblock, blocking adverts, but also self-updates as new advert companies come online. Works like a charm.
http://adblockplus.org/