How do I continue movement after a board element changed my orientation? Example: I may move three spaces in a straight line. A swirl rotates me 90° after my first move. Do I continue movement in the same direction as before (N/S/W/E) or in the new direction (N/S/W/E + 90°)?

The direction of your movement remains unchanged, even though your facing orientation is different. If you started moving North for example you would continue moving North after the whirlpool.