Hello Valkir,
Thanks for being a MultiBit user for the last 3 years !
3 years in Bitcoin time is an absolute eternity.
There are private keys in MultiBit HD but we don't expose them anywhere on the user interface.
For backups the most important thing to do is
write down your wallet words.
The wallet words shown to you when you create a wallet are enough to recover all your bitcoins.
We also generate encrypted backups of all the extra information to do with exchange rates, your contacts, transaction notes etc.
These are stored in the wallet directory automatically but for extra safety you want to set a 'Cloud backup directory' where these files will be copied to.
The idea of the cloud backup directory is that if you have Dropbox / SpiderOak / Carbonite set up you'll have a backup stored off your computer. If someone steals your laptop can recover everything up to your last backup. You need your wallet words to decrypt your backups.
The backups are explained in detail in the help here:
https://multibit.org/en/help/hd0.1/backups.htmlOh, one last thing. If you have more than a trivial amount of bitcoin, consider buying a Trezor.
The Trezor integration in MultiBit HD is really nice and then you won't have ANY private keys on your desktop computer - it's a lot more secure.