At step 2, you should copy the Master Public Key for the account (or accounts if you use more than the default one) instead of copying addresses. With that master public key, you can generate all of the addresses in that account (there are 2^31 of them so don't worry about running out of addresses).
To get the master public key, click Wallet > Master Public Keys in the menu bar.
Then, with that master public key, you can
1.) start Electrum on an online computer,
2.) click File > New/Restore in the menu bar,
3.) check the radio button that says "Restore a wallet or import keys",
4.) and finally enter your Master Public Key in the blank box that appears after clicking "Next".
If you do that, you'll have a watching-only wallet on the online computer, which means you can see all your addresses, your wallet balance, etc. but cannot spend anything because the wallet doesn't know your private keys. That way, you can always keep track of your wallet (you won't even have to use Blockchain.info since Electrum will tell you about transactions) without risking anything.
Thanks for the reply. So just to be clear, the purpose of the watching only wallet is to generate addresses and check balance, but It doesn't need to be online to generate addresses.
Is that correct? And can I send btc's to addresses generated offline that have never been broadcasted to the network?