Dont worry so much about her how she carries her head. you wont really be penanlized for it unless your at a larger show.
If you know she is going to pick up the wrong lead, why not just enter some walk/trot classes that way you wont get frustrated if it happens when your competing.
If you do enter the walk/trot/canter classes and she does miss her lead you will be penalize for it and probably wont win first place. If she picks up the wrong lead and everone else in the class pick up the correct lead, you probably will not place. But you can always use that as a learning experience. Personally I would work with her at home until I knew she had her leads down pat. Hunter under saddle classes are based on the horses way of going, suitability to rider and MANNERS. Not pickin gup the correct lead will be taken as disobedience.
As for her mane and tail you dont need to worry about it being braided. Her mane(if its just a regualr hunter show/ breed specific shows are different) does need to be short and even though, about 3 inches. For her tail I would say just wash and condition it well spray it with show sheen or some kind of hair detangler, let it dry and then brush it out. It should be gorgeous.
Good luck and have tons of fun!
~If horseback riding was easy they would call it football.~