In my case, I travel with two laptops and other items as well, they let me unstuff it all, put it on the scanner and wheel me through. They pat me down and wand me, while the one TSA employee collects my belongings in the trays and bag etc... and I repack it on the table next to me. They do not repack it for you unless you ask them too and they have never touched anything in the bins without telling me first and checking with me. When they have done further scans on my items while I was laid up the TSA employee stands by my bags and waits till I'm done with the wand and such to do the further checking so that I'm standing there with them. Are my eyes on the items, yes, am I next to them, no not at all times. On other times they have scanned everything first where I can see them scanning it, then took them over to the pat down area and then let me through to wand and pat me down where the items were waiting for me and they were in my sight the entire time.
Yes the brace will give you a pat down as we all obviously know and I have at times gone to pants where the legs zip off. First of all it's easier on the pat down if they see it, and secondly if you can take off the brace (not after 3 weeks but after a while) and take the four steps through the screener then you can take off your brace, walk though and then put the brace back on after it went through the screener. Might sound funny to strip a leg off but it does allow you not to have to go through the pat down / wand. If the pant leg does zip off they have asked if I could take the brace off and they scanned the brace itself, which is all fine with me, I am usually glad to get the brace off for a little bit.
And yes even after 3 weeks if the knee is still acting up I would take a chair; however I have been lucky enough that I have had good success with a cane which you might want to think about if you travel a lot after the surgery and such. A cane, if used properly, can aid you a lot in taking the stress off the leg. I still use my cane even though my last surgery was about 10 months ago; however I have had well over ten surgeries on my legs in my life, I stopped counting them when I was in my 20's

A metal cane must be screened but a wood one I've had them let me take it through the detector with me. I honestly am not sure what the rules are with that but I have both a wooden one and a metal one and I normally take the metal one with me as I can take the steps easily enough with out the cane through the detector.
Good luck and don't worry, there's plenty of folks going through what you're going through so most airports and TSA employees are well used to it by now (atleast the ones I've been through). I'll cross my fingers for your surgical success and that your travels are easy. The one thing I will say, if you have a wheel chair request, keep calling and verifying it is in your record, and keep asking when you check in that the other airports will have a chair waiting etc...