On my family PC there are lots of games, If I add them to my Steam account can I then play them on my laptop? Would I only be able to play on the PC they were on?
All that adding them to Steam does is allows you to launch them through Steam (and you will be shown as playing a non-Steam game to any friends you have). It doesn't allow them to be downloaded to or played on any other machine. Even if they were Steam games, you'd still have to download them from your library to the other machine to play, but non-Steam games don't allow for this.