Castles of Mad King Ludwig

No — a new Room must connect at least one entrance to an entrance on an already placed Room, may be rotated in 90° increments, may not overlap other Rooms, and you must keep at least one external entrance open (see placement rules) (page 9).

You resolve bonuses/penalties immediately when you place a Room — you score the new Room's bonus/penalty and any effects triggered on other already-placed Rooms as a result of that placement (pages 10–11).

Coins on a Room may be used as part (or all) of the buyer's payment to the Master Builder; if the coins on the tile equal or exceed the price, the buyer keeps any coins left over after paying the Master Builder; when the Master Builder buys a Room, their payment goes to the supply (pages 7–8).

No — you may not buy a Room if you have nowhere you can legally place it (page 9).

Downstairs Rooms can only be connected to the darker end of Stairs tiles, to other Downstairs Rooms, or to downstairs Hallways, and you cannot buy a Downstairs Room until you have at least one Stairs tile (page 9; details page 15).

A Room is complete when all of its entrances are connected to entrances on other Rooms (an entrance blocked by a wall prevents completion); when you complete a Room you immediately gain its completion reward, and you may resolve multiple completions in any order (page 12).