How is it that it costs nothing? The transaction fees are currently enormously high.
will the rest be sent to an electrum address and from this again to a new one of mine?
This is not exactly a feature, that's how Bitcoin works - if you have N coins on an address and want to send some smaller than N amount, the difference which is called change will be sent to one of your addresses in the same transaction. This change address can be the same that you were sending from or some of your other addresses, there is no difference in transaction size and fees. It is recommended to not use the same address as change address, because it's a security risk and it gives no benefits.
https://en.bitcoin.it/wiki/Coin_analogy