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Loading the front side of your back knee is going to cause irritation and inflammation of the surrounding structures. The torn bits of meniscus are impinging joint movement, as likely is that cyst--it's formed by fluid that's leaked out of your torn meniscus, pooled, and jellied.

Your meniscus injury sounds quite similar to what I had on my back knee's lateral side, and I have to be very careful about loading that side of my knee. I changed my rear foot's position to help with this.

I'm not sure about exercises. One risk is that, well, your meniscus is fairly shredded and it's getting in the way. Continuing to load that knee up might widen the tears and make the problem worse; you might want to ask the surgeon about that in your consult.