Thanks a lot ABCbits and Forsyth Jones. The information provided is very useful.

I understand that the Electrum server is *between* the Electrum client (=Wallet) and Bitcoin node. In fact, the Electrum server, after asking Bitcoin Core, fulfill the Electrum client request. Due to the decentralized nature of the blockchain, a full node is like a local copy of the blockchain. Am i right?

Still, and although it might not be safe, would it possible to tell the Electrum server to rely on a Bitcoin node hosted remotely by somebody that i trust? I know it might not be very good for the safety of the blockchain (if everybody does that the system becomes centralized), In other words is it possible for several Electrum servers to use the same Bitcoin node?

Also, is the only benefit of running (hosting) a Bitcoin node and an Electrum server is to avoid public servers (therefore ran by strangers) to associate a wallet with an IP? Also since my IP has already been associated to the btc transactions already made, don't you think it is too late? Only future transactions, and if never rely on a public server again would be private.

Cheers