1) The arrow is drawn to show the direction cosines that you entered. This should be along the major equipment axis.

2) There is a large write-up on local coordinates in the Technical Reference Manual - Chapter 6. When verifying the loads on equipment nozzles, the loads need to be aligned with the local coordinate system of the equipment (such as the WRC coordinate system). This is why you need those direction cosines mentioned in #1 above.

3) It isn't a forumula, it is a coordinate transformation, using the transformation matrix (based on the element direction cosines).