That should work.
The guide is unofficial but posted by a reputable member of Electrum board.
But when it comes to safety of the coins that you'll sweep, it still depends on the security of your machine.
2.
Does that mean, after creating a new Electrum wallet and writing down the automatically
generated new seed, the computer could be rebooted without loosing any funds?
You coins are basically backed-up by that seed phrase, it can re-generate all of your private keys even without that exact same computer.
PS:
After the funds have arrived in Electrum, I will transfer them to the Relai app, which is
linked to my IBAN bank account. This makes trading very easy.
In that case, regarding my note in #1, you may consider doing a cold-storage setup to send it to that app.
You can follow this tutorial for that:
/index.php?topic=5524213.msg64885706#msg64885706