If a horse it chewing on the reins, I wouldn't be inclined to hit him. I would be inclinde to jerk the reins out of his mouth so that is is not pleasurable to chew on them. If he is about to chew or play, shaking the lead or reins to get his head to move might help also as a warning.
If a horse pushes me, I would be a huge monster with no patience. A horse is NEVER allowed to use any physical force with me at all. In the field this means arms up, loud, firm and angry voice (not screaming). In the barn this mean poking him, stamping my feet and using the same voice again. I have NO tolerance for attempted physical intimidation or control from a horse.
If a he won't stand still when I'm tacking up -- hmm... that's tougher. I haven't had that happen. I guess it depends how he moves and what he knows. My mare knows the command "stand", so I would put her back in place and tell her to stand and it would be over. If persistent, assuming there are no pain issues of course and this is pure misbehavior, maybe keep pushing the horse in the direction he moved until you tell him to stop. You need, of course, to have a particular area/setup in your tacking area to be able to do this. You could maybe move him back and forth (or side to side) if you are limited in your area.
I generally reserve hitting for physical intrusions into my space, like biting as you have, or agressive advances. Generally, the level of misbehavior determines my level of discipline.
The horse that responds to "Quit!" or "No!" is one that has had a firmer , impressionable correction made before by the handler, such that the voice is enough to remnind it of the firmer discipline. If you've never done that to the horse, he has no basis from which to believe that your warning is really meaningful.
Horses really know who means what they say and says what they mean, and after that , a verbal warning is usually enough. Even then, they may still chose to push back at the handle, knowing that they are doing something "wrong", until they receive a really impression-making correction.
They problem wiht some horses is that it takes a lot to make that impression, and the handler that can't do that ends up in a position of "nagging" at the horse. How do I know? Been there, done that.
But, it also varies with the horse.
The thing is, in general terms, when you discipline a horse you have to do something that makes enough of an impression to make a change.
That change can be seen by having the horse really move, or really jump and maybe for a second be scared of you, or the horse can go from having their ears pinned to moving them forward. These kind of physical changes show a change in the mental state of the horse, even for a few secs.
As for chewing on the reins, one thought there is to stuff them further up the horse's mouth until he gags on them, and do this every time he grabs for the rein, and at the same time use a scolding tone of voice. This might make him change, but when you do it, do it hard enough that the horse really wants those reins out of his mouth, now!
As for him moving when you are girthing up, you could try first giving the reins a bob, and if that doesn't work, them move him briskly around. Make a lot of noise, slap you own thigh and stomp the ground. Think, "you wanna move? I'll show you moving!" and move him around. Backing him might be the most impression-making. Then offer him a peaceful place to be (and this is really important), which would be your standing near his side (not too close) and see if he will choose to stand still. If he chooses not to, then go back to moving him again. Stop him, stand near him peacefully for a sec, then go to girthing.
The other thing about disciplining a horse (in addition to making it memorable) is to catch it soon. When the horse is just beginning to think about this is when you can often catch and stop that kind of thinking with just a verbal "ah, ah, ah!". But it means you need to have one eye on your horse all the time.
When he starts to move a shoulder into you, he hasn't even moved a foot yet, you put a finger into his barrel and scold him and move him off. Next time , you just have to wave your finger at him, but you've got to catch him when he is just starting to act on that thought, when you first see it eveident in his body.
Practice watching your horse and what he is thinking on. you can use this under saddle, too. YOu can see/feel when your horse is thinking about bulging toward the gate or leaning in toward the instructor , and things like that.
It's hard to develop feel all on your own, and it's an ongoing process. Some trainers have amazing feel of the horse, like they were born that way. The rest of us just have to keep our eyes and brain open and work at it.