Is it normal for it to take 7 weeks for a strained knee to heal?

The simple answer is YES.Tendons take a lot longer than bones to heal.  Cut back on the exercises; is no lunges, no impact exercises, no knee bends.  There are a lot of exercises out there that you can do without working the affected area.  If you insist on doing your current exercises, even in a diminished way,the longer it will take to heal

Ice, Ibuprofen, rest, I listen to my body and rest when I need to but that is my last go to. I work my painful knee as long as I am not doing damage, I roll out and stretch the surrounding area and Ice immediately after workout. Ibuprofen is used very sparingly but used when necessary.  I am almost 69 and have had a TKR so sore is just part of the process, one day it occurred to me that I was going to be sore if I worked out or if I didn’t, so why not work out? As I age I experience pain in different parts of my body at different times during the day, the trick for me is it just old age pain or an injury. If it is old age pain then damn the torpedoes full speed head.  

I am amazed you wouldnt have been advised properly on some of these things like lunges. You haven't reached stage 2 of healing yet and are way ahead of the curve, which is fantastic but don't hurt yourself. I have found being overly aggresive and not paying attention to your therapist is the recipie for set backs. Having had to rehab 5 times has been a learning experience that has taught some pretty tough lessons. Stay with your program but be patient. You are still healing inside and nerve damage is far from completely healed. You are fortunate that you have the age, weight and previous physical condition to add to your positives. My estimation is you are in a category of less than 5 % who go through this proceedure. Most have had to reduce activities because of high pain levels. This of course, leads to being out of shape both physically and mentally. Best wishes for continued success.