The first six modes are for the solid body assembly, the next three modes are for the free standing remote point. The free standing remote point has only 3 modes because it has only mass and no moment of inertia. If you add moments of inertia, there will be a total of 12 zero modes.
A free standing remote point is not adding a fluid mass to the structure.
Is the fluid inside the container or is the container submerged in fluid?
I suggest you read this discussion for further information.