Yes, you may switch it out for another booster, but you cannot keep an empty board once you place a booster there. Hope that helps.
No you don't need a full booster board to be able to swap out one. You can click on the "modify" button (the one with the pencil in it). Then once you do that then you select the little arrow button pointing to "Badge 1". Note that the badge 1 position is in the center of the booster board. When you click on that button, a window opens up to show you all the badges you have available to use. (also note a green circle line around the center badge on your board, this verifies that you are selecting badge 1) You can place up to 5 badges on the board. Once you see the available badges you have, you click on the one you want on your board. When you do that, another window opens to show what level of badge you can place on your board. Select the level you want and it switches out. You now have a new booster badge on your board.This is a very useful link concerning the Booster Badge Board: https://crazybigfarm.net/