From what you've told us so far, I think you need to find a "teacher" that's LESS in love with playing with a $6k machine you will NEVER buy or need, and MORE in love with actually TEACHING. So far, he hasn't told you about ways of holding the gun, practicing MOVING the gun BEFORE you pull the trigger, HOW and WHY you do certain things and DON'T do others, or much else that beginners SHOULD learn first.
Seriously, if I were in your shoes I'd ask for my money back - you would learn far more in less (FREE) time at weldingtipsand tricks.com....
For example, your "leaning tower of pisa" welds - welds don't "pull" much at all WHILE you're welding, it's AFTER - they're caused by SHRINKAGE, and since the side you welded got the most heat, it will SHRINK more and "pull" the welded piece to that side - sometimes DRASTICALLY, as you experienced. There are a few ways to combat that, some will help right away - others take quite a bit of experience to COMPLETELY eliminate the problem.
Some of the ways that work for me - set the piece you want at 90* to a slightly OBTUSE angle on the side your FIRST tacks will go, then quickly tack the OTHER side - keep moving your subsequent welds around, constantly checking "square" as you go, placing your NEXT weld on the "obtuse" side -
I've done a lot of projects using square tubing, and when it's possible I will HARD clamp a diagonal across 2 pieces I want SQUARE (but STILL use the "hop around" and "let it cool" tricks) - I've built several "roof frames" for portable shelters, typically 8' x 12', some 12' x 12' - using these "tricks", they are ALL less than 1/16" difference in diagonal measure. Find me a WOOD framing carpenter that can claim that
Here's one example of combatting weld pull -
http://www.tractorbynet.com/forums/welding/314087-preheat-advice-requested.html?highlight=
Jody (weldingtipsand tricks.com) will tell you to "stay at the front of the puddle" and "push" weld with MIG - those two things will get you further than most comments, and if followed religiously will keep you from "piling bird poop on top of MORE bird poop" -
There's a bunch more to this as anyone will tell you, but it all helps... Steve