You can generate addresses even now. You don't need to have electrum running. There is some code here:
https://github.com/prusnak/addrgenBut to learn about coins you've received you have to have bitcoind or use blockchain.info's api. I suppose you could use electrum as well but you'd need to know python to fix that merchant script.
Electrum can be run over the command line. No gui required
Electrum 2.0 is going to feature a full featured daemon process for servers:
https://bitcointalk.org/index.php?topic=427617.0There is no electrum network fee but if you want to support the electrum servers you can donate to them. You'll find their address on the console tab in the Electrum window.