How will the water surface of this planet looks like ?

Lets suppose we have a planet made from two half-sphere with the same radius (R) made from matter with different density.

The left-half-sphere is made from rocks (5gr/cm3) and the right-half-sphere is made from iron (8gr/cm3).

Then we pour water on up to about one-tenth of the sphere volume.

1. Will the water collect up to a surface with the same gravitational acceleration or collect to up to a surface with the same potential energy per mass level ?
a. assuming the planet isn't spinning
b. assuming the planet is spinning along the rocks-iron line
c. assuming the planet is spinning along a line perpendicular to the rocks-iron line

2. What is a class of geometric shape experiencing the same gravitational acceleration magnitude given the position and mass of several source of gravity (lets assume it is point-mass for simplicity)? ( Yes, I know the shape would vary a lot depending on the system. I want to know whether there is any standard name for these class of geometry. )

I need these information in order to calculate the shape of Rocheworlds and Roche-Klemperer-primary.

Thanks for your help,


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