For the rearing it certainly varies on the horse.
My first mare I taught to rear on my own (after going to multiple Medieval Times shows, lol), when she offered a rear without a cue I took the reins to both sides of her neck quickly and sharply. Scared her half to death and she never did it off cue again. (This was a no higher than cannon bone rearing horse).
I had a TB gelding I was training for someone who reared when I took him from his buddies. All I did was push him forward, got his feet moving, he never offered it again.
The downside to my post... I had a 4 year old that was a chronic rear(er) because a friend of mine thought it was "cute" to teach her to rear from a young age. I tried everything from smacking the crude out of her, getting her feet moving, pulling her to the ground when she reared (with me on her!), etc. Nothing worked. She ended up flipping on me, crushing my ankle and breaking my knee as an end result. I never touched her head to discourage rearing (though I have heard the egg/water balloon trick works) because I was concerned it would make it worse than it already was. I wouldn't be surprised if she was on someone's dinner plate in another country. She disappeared from WV a few years ago.
Please, please, be careful with rearing. It is a nasty animal.
The Fluffy Equestrian
Rhett | Hang on "Fiona" | Rockstar
Reg. TWH Gelding | Irish Draught Horse Mare | SSH Gelding