You did not import your wallet into electrum.
You created a new electrum wallet and imported private keys from your core wallet.
There is no seed option because you have imported private keys.
To use the option of a seed you have to create a new wallet and send your funds to your new wallet.
Yes.
There are a lot more ways to protect your holdings.
You first have to know against what you want to be protected.
You should create a new wallet and use the seed option. This makes backing up your coins way easier.
Transactoin fees can't go lower than they are nowadays.
If its only because of the space.. you can use prune mode. This way core does not store the whole blockchain.
If your backups are correct (you have tested them), you can safely remove core from your hard drive.