I didn't have that surgery, but I had half of my knee cut out to reshape it because of weak vastus medialus. Also in the same (left) knee I had meniscus removed to the left side of patella.
At my highest ever I did 1RM 180kg squat and 200kg deadlift, they are not that much different weight wise, since my knee is the limit. At the moment I squat around 110kg and going up, since I'm recovering from few broken bones. I'm planning to settle at doing ~125kg for reps, I don't need the huge numbers I did in the past, since I want to preserve my knee as I'm 35 and I had the knee surgery 10 years ago.
What I do is take 8g of fish oil per day and 6g of glucosamine per day. Few studies say that the later doesn't do anything, but without it I would be barely able to walk up stairs, I will not even mention lifting weights. And yes, I had stopped using it few times and I had to start it back up. Experiment for yourself and see what works.
Lifting wise it seems to me that you have weak VM. I would concentrate on getting your formed nailed first, since weak VM means bad form. Are your knees to the outside of your toes? Or are they collapsing to the inside when you are coming out of the hole? The later means weak VM. Are your knees behind your toes? Have you read Ripptoe's Starting Strength and watched his videos on youtube?
If I were you, I would get a Olympic or Powerlifting coach to see you through this movements. That's what I had done in the past, it's a worthwhile investment that will pay off in years of being able to train.
The number of people I see in gym doing this mistakes makes me cringe and I get pain in my knees just looking at them. Just last week in the gym I go to I saw one of the personal trainers teach one of those guys who has massive upper body and no legs (I'm the opposite at the moment) teach him how to squat. This guy was teaching the guy who has never done squats really bad form from the start. I would say 99% of personal trainers don't know how to squat, so don't ask them unless you are looking for more knee surgeries.
Also good shoes are important, throw away your soft running shoes with 0 support. Get Converse Chucks or something with very hard thin sole. My next purchase will be Olympic lifting shoes.
By the way, I squat 3 times a week and my knee is doing fairly well for the past 10 years. I would also avoid lunges if I were you, they are hard on knees.