The imbalance is probably the source of your back issues.
As you squat, you'll favor one side. The imbalance will just get worse and worse.
You've got to stop using the big compound moves for awhile, and get into tons and tons of single leg work.
1 Leg Extension
1 Leg Curl
1 Leg Press
1 Leg Calf Raise
Not being able to raise your legs symmetrical shows that your abs/obliques/lower back/hip/glute muscles are not working together properly. The two sides or your body are moving differently, that's why your feet don't line up correctly. You've got to get those glutes/adductors/abductors/psoas working properly, 1 side at a time.
Seated Psoas Hold
Peterson Step Ups
Terminal Knee Extensions
Standing 1 Leg Calf Raise
It's even possible that you are walking around with 1 shoulder higher than the other. You need to work those lats/rhomboids/traps working correctly on both sides. Try
Rear Delt Raises
1 Arm Shrug
1 Arm Row
1 Arm pulldown
Also, don't forget 1 arm farmer's walk and sidebends. Basically any lift you can work one side at a time. Use the weak side for all sets and reps first, then do the strong side.
Check out this great article by Chris Colucci about training for symmetry
And this one, on a "different" way to structure core workouts