So i understand in Electrum by pressing sweep and adjusting the fees i can avoid the too-low-fee danger of Multibit alltogether?
In other words; i don't need Multibit at all for sweeping the coins? That would be fantastic.
Correct. Be sure to keep Replace by Fee checked.
And after it is done and i checked and doublechecked that the coins are indeed safe and sound in Electrum can i just uninstall Multibit and free up the tons of space?
Yes. Keep a backup of the wallet file from MultiBit just in case. There could also be coins from the other Bitcoin forks as well, Bitcoin Cash, etc. The value of those is quite small and might not be worth your time and effort.
Also, what do you mean with Sign and Broadcast? Or is that self-explanatory in Electrum?
Finalize there:
Sign and Broadcast. You'll only be able to broadcast after clicking sign.