rotational mechanics doubt

1)Consider movement of earth about sun(consider it is in a circle).
Now axis of revolution passes through sun, and angular momentum due to revolution is parallel to axis,
but the earth is also revolving about its own axis that is not parallel to the axis passing through the sun.
Hence total angler momentum=sum of both components and the net is not parallel to fixed axis.

Thinking about 2nd part..

but what about particles in a rigid body?

is this what it has to take something from...?