I have question why local coordinate system not working for points load or for poits BC and for gravity load?
Local CSYS assignment internally transform the coordinate system of the nodes used for the boundary condition or load definition. It can be used with concentrated forces abd BCs, but not with distributed loads such as gravity.
If it doesn’t seem to be working for some reason, make sure the local CSYS is not only created first, but also assigned to the BC/load definition (instead of the default Global).
It doesn’t work when applying a BC via rigid body constraint though (due to CalculiX’s bug/limitation): Potential Bug Applying Radial Displacement to Rigid Surface