How do you restore health on your partner, like lady Shizuka???? I don't want her to die and then I completely mess up the game somehow, but I'm not use to mmo's and that stuff. So I wasn't able to find it anywhere really. Can I restore her health? Or do I wait until she finally passes out and then she auto revives when I find a safe location? Any suggestions/tips?

In this beta as far as I know, you can only dismiss them and they will slowly heals over time or you can just let them passed out and they will slowly heals (I usually dismiss them when they're at 50% of their hp, most of the time, I never use my partner because I literally forgot I have several.)
There's no auto revive for partner, you have to wait for their health to be restored to the max if they have passed out, so I can only say is that try not let them die and if you're cautious you can dismiss them before they reach less than 25% of their hp.
There's no other way around this and there's no hp items that can be consumable to heal their hp.

I found that if you go into the Partner screen and choose the "Dismiss" option (or summon a different partner), partners will recover their health while "sitting on the bench". It may not be very quick, but it does let you do something without forcing them to take a few swords to the face.

They, from what I could tell, don't recover while summoned, even if not close to combat. So dismiss your partners whenever you go into town and let them rest when you aren't expecting a fight.