First off, did you get seen by an ortho physician or PT/ATC/Osteo for evaluation of your knee? Unless you completely dislocate you knee, it is VERY difficult to injure/tear your MCL and LCL at the same time. If you haven't seen a healthcare professional about this, go see one. For all you know, you may have injured your ACL, meniscus, or other structures.
For your "rotated knees", from the picture you posted, on both knees you have some valgum ("knock kneed") occurring which is associated with hip internal rotation (I am assuming that you are referring to your hip rotation when you say leg rotation). I'm not sure where you were getting that your left hip is externally rotated. Also, an internally rotated hip will place additional stretch/stress on the MCL, not the LCL.
The solution you are trying to use to fix your lordosis should also help with your valgum knee position and internally rotated hips. Strengthen your glutes. The single leg (pistol) squat is a poor test for glute strength as it recruits the quads more-so than the glutes.
After getting checked out by a doctor to rule out any significant injury and to find out exactly what you have going on, I'd recommend getting your movement quality, mobility, and strength screened by a qualified (strength) professional. From there you can determine where you should focus you training to fix your imbalances and the best/most efficient way to go about it.