I have downloaded a copy of FinalCut Express Pro but cannot do anything with it, because I have no registration number. If I cannot use it, why is it downloaded on LimeWire?

Any user of limewire can upload anything they like. Limewire is not responsible for the files on the net work.
There seem to be many files out there that knowingly or unknowingly to the uploaders are useless.The safest and most reliable way to obtain commercial programmes is to obtain them from a known source. with a p2p netwiork you take your chance. The worst that can happen is you download a virus so take care!