Ok.. I understood about addresses, thank you for your explanation.
And what about this connection trouble?
Is there any other way to use my money if the program doesn`t want to connect?
Maybe some online interface from browser or another program which can restore the same wallet or... whatever?
You can export your private keys from electrum and import them into any other wallet and take control of your bitcoins, if you're looking for a web wallet which does this then you can use blockchain.info wallet's import wallet feature, although I wouldn't recommend it because web wallets are not as safe as electrum is.
Another way is making a raw transaction with electrum and broadcasting it with blockchain.info's push transaction, that way your keys and btc remain safe but you will have to do that everytime you want to send bitcoins which can be a bit of a hassle.