I doubt you could pass a medical if you need crutches to walk into the doctor's surgery. Meniscal tears come in all shapes and sizes and only the doctor who has examined you and looked at any imaging can tell you how long you will take to recover. The best thing to do would be to ask him.
The good news is that even if you do need surgery these things can usually be fixed and it usually doesn't take long to get back to normal. I would say that if your doctor recommends surgery, the time it takes to have the procedure is more relevant than the time it takes to recover after having the repair i.e. waiting lists.
There is no reason why you cannot have all the other tests and assuming you pass these, have the medical certificate issued when your knee gets better. If I was you, I would continue with your studies and not worry too much about your knee.