Well definitely when she gets into your space be very stern and make her back up, show her you are in charge. Once she has backed up and done what you want tell her she's good and walk her forward. And repeat this each time she gets into your personal space. Hope this helps!!
Showmanship is one of the best things to do with a young horse or why horse for that matter, it earns your horses respect and is overall a great skill to know! There are many videos of clinics and suck on YouTube that you look at to teach yourself!
I do ground work every time I go see my horse. Have a read at Clinton Anderson's Downunder Horsemanship. Very helpful and my horse has improved so much from it! He only eats when I tell him too 🙂
We got an untrained horse at my barn and we use a chain that goes across his nose. He seemes to listen to verbal cues I taught him and a sharp tug on the lead when he does something stupid like try to eat my hair or eat the grass
You can make it harder for them to misbehave and easier to behave, by applying pressure when they do the wrong thing and releasing it when they do the right thing
My horse used to do all of those things. With time he learned to tell apart the "work" moments (when he's not supposed to walk around or graze) and the "free" moments. Reward her when she does what you want and insist when she doesn't. Horsemanship in the round pen and the paddock also helped a lot for me.