Re: Knee issue - meniscus tear
Do you know what type of meniscal tear you have? Depending on this, the goal for surgery can vary from stitching to repair, or outright removal of the tear/flap.
As far as surgery goes, there is no reason why you cannot continue to train after an arthroscopy, with reasonable lower limb input including squatting/deads, indeed building the muscle around your knee is vital if you want to offload the strain put on the joint. There will obviously be a recovery period, but an arthroscopy and meniscal tear repair is a fairly low risk operation in general, if that's the isolated damage. Knee extensions are not a great exercise for ligament damage due to their open chain nature, but if you want to maintain movement control then closed chain will be excellent, and to be fair even open chain will likely be ok after recovery providing you don't experience discomfort doing them.
Regarding arthritis, most knee injuries are linked to this. Ligament tears, meniscus tears, blunt trauma to the patella etc. I've torn my ACL, but worked bloody hard after surgery, and I'm squatting heavier than before, back to reasonably high performance levels with my rugby, building more muscle around my knee - especially posterior chain (consider glutes as well). I'm probably going to have an arthritic knee at some point, but I'm positive I will avoid it for as long as possible by doing everything else right.
If you can't do the stretching at the minute (I assume heel to backside?) look at going into a lunge and lessening the knee range of movement from full to around 90. Stretch at your hip and foam roll at your knee. Invest in soft tissue massage, free up your quads/hamstrings/glutes/lower back and take the time to work on mobility. Get the supple leopard book from Kelly Starrett and bring your rehabilitation work on your tight areas and restrictions - if you want to avoid further injury and poor outcomes, take charge and optimise what you can.
Finally like I say, I wouldn't stress about surgery. If you do things right the outcomes are generally ok, and you can get back to fairly normal activity. Ask the consultant if he can do the operation rather than his SHO/reg as your sporting performance is important to you, and good luck!