Is it really necessary for the orbital plane of a satellite to pass through the center of mass of the object around which it's orbiting? Is it really necessary for the orbital plane of a satellite to pass through the center of mass of the celestial body around which it's orbiting? Does the answer depend on, whether the celestial body is a sphere of radially symmetric density or it's irregularly shaped (for example, a comet or an asteroid)? If there exist cases where the orbital plane doesn't pass through the center of mass, how is Kepler's First Law defined for such cases, since the center of mass of the larger body doesn't lie on the orbital plane of the satellite which contains the foci of the elliptical orbit?

Please Note: The answers for the question Why do satellites orbit around the centre of a planet? did not clarify my above mentioned doubts. 
 A: It is absolutely false that the orbit of a satellite should always be a curve in a plane. And it is also false that the direction of the force should always point towards the center of mass of the attracting body.
As far as the first statement, it should be noticed that in the case of central forces the existence of a plane where the orbit is confined to stay is ensured by the conservation of angular momentum. If the attracting body has a spherical distribution of its mass, a mathematical theorem ensures that the resulting force is central and the situation is equivalent to concentrate the whole mass of the body in its center of mass. However celestial bodies can have shapes deviating from the spherical one and/or a non spherical mass distribution. As a consequence,  real interaction energies, in particular at small distances, can be far from being spherical. A general description of anisotropic gravitational interaction, like that felt by low Earth orbit satellites, can be described by a multipole expansion. In such a case, angular momentum conservation does not hold and there is no planar orbit and no Kepler's first law.
A part the angular dependence of the potential energy, it is also interesting to notice that in general a non-spherical mass distribution does not attract in the direction of the center of mass. This can be easily verified examining simple examples of non spherical mass distributions.
