Momentum of solar panel after photon is absorbed 
A solar panel installed on a car of mass 1 kg lying on a friction free road. Let the efficiency of the solar panel be 100%.let the momentum of photons be $m_o$ and and the car be at rest before collison.

After the photons absorbed by the solar panel and converted into energy, will the car move due to conservation of momentum? 
 A: You are asking whether a photon can excerpt pressure on matter it interacts with.
When a photon interacts with an atom, three things can happen:


*

*elastic scattering, the photon keeps its energy and changes angle

*inelastic scattering, the photon gives part of its energy to the atom and changes angle

*absorption, the photon gives all its energy to the absorbing atom and electron
The answer is yes, even when a photon hits a mirror (and gets reflected), it can excerpt pressure on the mirror by transferring part of its momentum to the atoms of the mirror.
Now in your case you are asking about a solar panel. Now even if the solar panel was a perfect absorber (it is not), and it was absorbing 100% of the incoming photons, some of the photons' momentum would be transferred to the atoms of the solar panel, thus excerpting pressure on the panel.
Now since the solar panel is not a perfect absorber, all three things happen with it, elastic scattering, inelastic scattering and absorption. 
You are mixing two things, energy and momentum. Some of the photons' energy is absorbed by the solar panel, some are reflected. But in all cases, part of the photons' momentum is transferred into the atoms' momentum of the solar panel, thus excerpting pressure on the panel and eventually moving the panel (if it is enough momentum to move it).
The car in your example is too heavy, and there is too much resistance from the road. This will never move the car in a measurable way.
But if you would have your solar panel in space, then yes, the pressure excerpted by the photons that interact with the panel, would give the panel enough momentum and would move the panel. This is how solar sails work.
A: As you realized, the two conditions you impose cannot hold at the same time. If the car moves due to the photons the energy conversion to electric energy cannot be 100%. For a macroscopic analogy, if you throw an object at a fixed wall and you have a plastic collision, all the KE of the object is converted into internal energy (thermal energy). If the wall can move, you cannot convert all the initial KE into internal energy. Some of it will be "used" as macroscopic KE of the wall. 
