a) Divide the player's position by the size of the tiles (do this for the x and y axis). The result(as an integer) is the tile the player is currently on.
b) Have a bool variable for each tile. Have the variable be true if the tile is cross able and false if the tile is not cross able.
c) Implement a collision system using the four vertices of the tile to get the bounding box rather that the predefined getBoundingBox() function.