Your tale sounds like the typical first time pilots adventure. The good news is that your not doing any worse than the average learner so just be patient and soon you'll be in a hover in no time. As far as the head wobble goes the mainshaft is pretty weak as it is made out of aluminum so it bends easily. Even just a slight blade scrap is enough to put a slight warp in the shaft. Take off your blades and spin it up with just the flybar and look down at the head and see if it's out of balance. Make sure the flybar paddles are on all the way and equal distance from the flybar carrier. Also make sure the paddles are level with the ground.

Anytime you upset the balance of the blades you are introducing wobble to the head because of the imbalance. If just the covering is missing you can either CA or scotch tape the ends providing you balance the blades afterwards. This will help you get more flight time out of slightly damaged blades and keep the learning curve less steep instead of waiting for replacements. If you check around Ebay or Tower Hobbies you can get plastic trainer blades for the Axe. They are pretty durable so they should last awhile. One other thing, The Blade Cp tail rotor blades are pretty much a direct fit for the Axe and at 2 bucks a piece you can buy a few to throw in the field box.