Of the "sites" you list, btc-e, bitstamp, and campbx are commercial exchanges. Localbitcoins matches up individual buyers and sellers. And coinbase is a middleman service between users and a commercial exchange. The other "sites" are merely ways of sending fiat from one person to another.

Your questions show some misunderstandings (that your coins are somehow stored in you computer, for instance). They will be easier to answer if you first read Getting Started With Bitcoins.