How many displays are connected to the client and to the server machines?
Are you connecting to the physical desktop of a Linux server?
I can be wrong, but in my opinion it is client settings and not related to server.
Client simply does not remember windows size.
But if that matters I tried 2 different machines, 1 headless with [removed], 2nd one with 1 physical monitor, but it is not used and connection is made to VNC session.
As for your second question, the client doesn’t normally close the window with the list of connections while other client windows are running, so I’m not sure about what you’re seeing on Windows.
On Windows I used previous version of NoMachine, probably 7.x, now I updated to latest one 8.8.1 and situation is the same as on Linux. I think you changed that behaviour. So is it possible to close window with connections automatically after I connection to some server is established?