How do I delete a waypoint
 

Been searching this forum for the answer and the manual but I can't seem to delete waypoints from my course, SH3 had a specific eraser function but SH4??

There's an eraser (which looks like an eraser) at the bottom left of the navigation map screen.

Clicking on the eraser will turn your cursor into a small eraser. You can then click on selected waypoints in order to delete them. Pressing SHIFT and clicking on any waypoint will delete all of them.

Can you move them, never lets me.

Sure. You click on the course plotter icon and place your cursor over the waypoint. Then you left click and drag the waypoint anywhere you want.

You click on the icon you use to ADD a waypoint? Wow, wierd UI choice, never would have occured to me in a million years (I'd have had the hand to drag work everywhere except right on a waypoint, in which case it would drag the waypoint).