License questions...

I have my full version installed on a computer that I won't be using anymore. I'd like to get FF running on my new pc and also get another copy for my girlfriend to use on this pc. What's the best way to go about this? Can I transfer this license to her, or do I have to use it? I installed a demo on my pc to get me through but it has stopped working (after 2 days). Tried entering my license key and I get an error saying it's invalid.

I'd also like to know about internet sharing and FF. We'll be splitting the internet between the two computers... will we both be able to upload/download filters, and update?