I also regularly get these 'This accessory may not be supported" problems. I do use a lot of different cables. Really a lot. Mostly certified aftermarket cables, sometimes apple cables, sometimes non certified ones. I found out that the device doesn't always complain directly. Most of the time it accepts the cable for many times, and then starts complaining with the same cable sooner and sooner. Odd, I admit.
AFAIK there are (not yet) 3rd party aftermarket SSD upgrades available for any MBA's from the 2013 model year on. I mostly doubt that that Samsung SSD you pointed out would work, as Apple use a proprietary technology for its PCIe SSD's.
Even with a non-retina screen it's nearly impossible. Even *if* you get your screen assembled back together and in a working order, chances are high the rubber bands are not 100% in line, which will result in something far more ugly than your dirty Apple logo. Please don't risk that.