hi - great post and great detail !!
Please remember that it is hard to be definitive when i haven't examined you (all the usual disclaimers )
It would seem that your left hip indeed is not working properly. It may be from the osteoarthritis or the osteomyelitis. It may be from a tight hip capsule or muscles. There are many different possible causes of the problem.
However, one of the observations is decreased hip joint space. That sounds consistent with your descriptions of what is happening functionally (during squats, sitting etc).
You are right, the left hip stopping during your squat is not ideal for your back - it places an uneven load on the whole body.
The real question is whether you can control the hip better. This is hard to test - even physios have trouble knowing whether the hip is centred during motion... The most common movement during motion is an anterior glide - this is where the hip should sit centred in the socket but it slides forward. When this happens, it pinches against the cartilage (labrum) and can cause the joint to painfully or not painfully stop moving.
The external rotation you have in your hip during sitting could be because it has run out of space to flex and so has to roll outwards to find room for the hip to accommodate your sitting.
As for the weights, that type of exercise is not necessarily indicative of your true hip strength in standing etc because you did the tests lying down. In fact, those tests claim to be muscle strength tests but they also test your coordination, joints and beliefs! For example, if i did the test and you had perfect muscles but a broken leg, you would test "positive" for weak muscles. In the same way, if your coordination is off, you can test positive. There have been different types of studies which show the effect of encouragement, beliefs etc on performance...all of this i guess is to tell you that you aren't necessarily weak in your hips...maybe your right hip is tired of catering for the left hip!
Anyway, you need to find someone who knows how to assess your hips and whether your coordination and joints are ok...that will not be so easy Once you have found that person, you will be able to get a better idea on how to strength your legs safely.
Hope that was helpful for you
Cheers!