I want to post some photos on FB and have them look as good as possible.   Should I upload full size and let FB resize, or should I resize to FB's max displayed size (whatever that is this month), and sharpen at that size,  before uploading?

It's hard to know what to do because they're continually changing things.   And if you Google for answers you find all sorts of out-of-date information.

I think it is important to size the images for the frame they need to fit. For example my Cover photos are sized to 851 x 315 pixels (ratio 2.7:1), brightened and saturated slightly more than usual (because apparently FB puts a 1% or 4% 'greyscreen' over the images which noticeably dulls them) and then sharpened, again slightly too much.

I havent noticed any dulling. Only pixelating

Sounds like you need a new monitor then. Trying opening the same image that you have on your FB cover and also on your HD and view them side-by-side. Even on my crappy little laptop the difference is obvious.

1200 pixels long edge is optimal.

1200 pixels long edge is optimal.

Why do you say that?  I just checked, and it seems like 960 pixels is as big as they will go.