1) How can you run a full node wallet with electrum? what do you need? Or please link me to an understandable guide for that
This probably should be a separate question.
2) Do you have to be online always or can you set it up, fund your wallet, and leave it offline for months, and just from time to time use it for transactions?
You can use it only intermittently if you want, but the full node will need to synchronize with the chain. If you're offline for a long time this can take minutes or even hours, depending on your hardware.
3) Is electrum the only software you need? Or do you also need bitcoin core?
Electrum is a wallet, not a node (and much less a full node). You need to run a full node (e.g. Bitcoin Core), an Electrum server that can serve Electrum clients with data from that full node (e.g. Electrum Private Server), and then connect your Electrum client to that server.