The clicking/popping noises are probably the tendon being tight that is flicking over a bone.

The core exercises are all well and good initially, but then you need to make them more specific. Your problems are push-ups and pulling accross the body, so strengthen up these two actions. Start with push-ups against the wall like you are doing but progress towards the floor then on knees and full length. Use the thereband to mimic the other exercise.

I would also work on some proprioception, ask your PT for some exercises.

I would have thought that a tear would have healed, but without seeing you I wouldn't want to say for definate.

Karen