Take the head issue - She pushes her head up to you (nudges) which could be for one of a few reasons - either she is itchy and wants a scratch, she thinks you may be holding a treat, she wants to be on the far side of you... etc. If she is itchy (like after you ride) then ONLY scratch her when she hasn't touched you first. If she does nudge you then walk away or bonk her on the nose (firmly but don't hurt her too much). If she is looking for a treat then get her to stand back from you before she can get the treat. Push her back until she is far enough away from you, say stand and let her stew for a second then give her the treat, much as you would if you were teaching a dog to stay. If the nudging is really ingrained then sometimes a good knuckes to the hard bit of the face will work wonders to get her to listen
The key is consistency and time. She will learn if you are consistent but you CANNOT let her do it some days and not do it other days, this just negates all the good work you've done.
Horses also have pressure points where you can extert a small amount of force that will not hurt them but make them uncomfortable enough to back off. One is in the center of the chest. Stick a knuckle in it and give it a strong push and the vast majority of horses will back up. Ask your trainer where the other ones are, they will help alot in terms of getting the horse to move where you want it too.
After that you can use the pressure points to put the horse where you want her while you're grooming and then use them to make her stay there. Your best bet is to pin her between you and a wall/fence so she has to move towards you to get out and then you can move her back in before she gets very far.
If she does move when you're grooming her then make sure you're not using a brush that would hurt her. Try a softer brush for a while and see if it makes her more comfortable - we have a horse who never gets anything more than a body brush because his skin is so thin he gets really upset if you use a stiff brush on him.
I hope some of this helps. If you are inexperienced I would recommend getting a trainer or someone with more experience to help you learn how to fix ground manners. She may not mean to hurt you but she is bigger and stronger than you and the pushyness can put you in a dangerous position even if the horse didn't intend it to do so, therefore it's better fixed sooner rather than later.
Edit: I also meant to add that as far as I'm concerned none of my horses are allowed to touch me without me touching them first. We have many cuddles and scratches but I choose when they start - not the horse!