1) What can the owner of a full node see when I connect to his node?
He should be able to see your public IP address that's why it's advisable to make use of VPNs like Tor to mask your iP and Also anonymise your connection. Nodes you are connected to should also be available to view your node compatibility, and connection with other nodes. If you are making use of a wallet, nodes you are connected to will see transactions you broadcast and they can also rebroadcast the transaction if it isn't confirmed.
What can the owner of an Electrum server see when I connect to his server?
Likewise for Electrum the server should be able to see your IP address, public keys, your transaction history and UTXOs and also you Version of Electrum.
However they obviously can't see your seed phrase or private keys as well as your wallet encryption password.
Some people prefer to run their own mode too if they don't want to share any of these details.