Ooo, I'm the first
Ok, so....for the pawns first. IF you are in modeler you can just hit F3 to drop to floor which is usually the y=0 plane. There is also a function in layout called Gravity that lets you select the direction of the force, the frames when it's active and also the nature of the oject (rubber-bounce led-bounce-less kinda

) but it has to be added for every single object so it's probably the best idea to select each pawn in modeler and hit F3.
As for the squares not rendering... do you by any chance have two plane objects there? The chess board and another plane? If that's the case than maybe you need to move the chess board up a bit or the plane down so they don't superimpoze or something, not sure how to explain better...