Maybe she's kind of dry - which would cause her nose to get dried out (dry boogies are itchy). Push fluids - give her a cool water bottle (or let her pick one out) and with alot of fluids her nose, eyes and skin would be less dry. When my daughter was in 3rd grade she used to lick the palms of her hands. It was gross. I tried using antipacterial gel to give it a bitter taste - but she'd go to the sink and rinse it off. Eventually I figured out that her hands just felt really dry - so we tried a few different moisturizers until she found one she liked (Mary Kay - go figure) and she was cured.
As for the temper - kids use whatever works. Subconsciously they begin to realize cuase & effect and if a behavior gets her waht she wants (attention, a treat, a food, etc.) she'll use that behavior more and more. My daughter was also one to have these huge meltdowns over stupid minor stuff. I begn to jsut pick her up and move her to the side (of the room, into her bed room, whatever) and ignored the temper tantrum. If we were in public we'd just leave and go sit in the car. I'd read something or clean out my pocketbook while she raged in teh back seat, or her bedroom, or the hall outside the kitchen. If she moved herself into the middle of the room whre I was I'd move to a different room. I didn't get upset, I didn't scold - I just ignored. After a number of episodes (5 maybe?) she began to realize she wasn't getting what she wanted. It stopped. She's now 16 and we have had some skirmishes over the years since then. Age 14 was really tough for us (first year of high school) but we kept doing the same thing - encouraged the positive and ignored the negative (when appropriate - soemthings required consequences like losing priviledges).
As it regards the temper - she needs to understand that you and dad are the boss - not her. She needs to know that even if she can't control herself that you can. Calmness and ignoring negative behavior seem to work best. STaying calm is best - but not easiest - that's for sure!
Good l uck mama - this parenting stuff is so much harder than I ever realized!!!