Re : Planarity of ATE socket Mounting & Donut pad of socket

ATE Test sockets for production use are expensive.  If this fixture is used for testing over temperature range, the pcb usually falls apart(delamination) in six months from being cycled from 0 to 130 deg F once or twice a minute using liquid nitrogen.

Sockets are also not supposed to be soldered to the test board.  Having copper exposed in all areas where the socket touches the board probably minimizing warpage of the socket or the board.  Sockets are expected to last longer than the board.   Remove mask where the socket touches down.   One more safety item that reminds me not to put passives where the socket body will interfere.

which is good.  Those fixtures are usually hand-assembled and expensive to spin because I screwed up.

Planarity mainly refers to the flatness expected under the socket (the top side of the PCB). This is kind of a carry-over from the old mechanical mentality whereas the mechanical engineer would want the surface to be "as flat as possible". It kinda is, and will be. The sockets are generally not large, and mounting a nice, solid hard plastic socket to a board will pretty much assure flatness. But, you want the board to be as flat as possible in the socket area so all the pogo pins (or whatever your interface from the socket to the PCB is - could be elastomeric material, I don't know) will touch down properly and make good contact with the board. Good day.

Some folks even dimension the area like what's called out in the socket pad pattern detail, but I see that as a little overkill. But to each his/her own.