In either case the player must be able to move across it. The replaced tile is recycled to the bottom of the stack. Once all spaces on the board have been filled, only replacement moves are made. The removed tile passes to the next player for use. Tiles are always replaced, never just rotated in place.
Runners move along the paths crossing the tiles.
They always go all the way across a tile. Where paths cross, they are underpasses and overpasses, not blocks. Where tile edges meet or are extended by external detours printed on the board, the path is continuous. A runner may move in any direction on the board, but may not re-enter its starting circles nor enter any other player's finish circles. A runner, in crossing the tile placed on that turn, may return via a loop to the stop it just left.