If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and B having different temperature: A: having only internal potential energy and B having only internal kinetic energy, can heat flow from A to B ?(temperature of A > B)
Yes. According to the accepted theory of gases, a diatomic molecule (like N2) has both translational kinetic and rotational kinetic energy, five partitions (two rotation axes, and three directions of travel in space), which each can hold kT/2 energy, on average, for a total thermal average energy of 5kT/2. A neon atom, on the other hand, cannot hold rotational energy (it is too cold, at any ordinary temperature, to hold one quantum unit of angular momentum along any of the three directions), so holds a total thermal energy of 3kT/2.
So, air (containing both neon and nitrogen) fits the description.
Different amounts of energy at the same temperature means different heat capacities, there are many examples (and this is only one).
If a body (substance) has zero kinetic energy then we should suppose that it is a perfect crystal at absolute zero and all motion is in the vibrational ground state if it is a molecule. If an atomic solid then only zero point motion in the lattice. So yes it has a temperature. The potential energy is that within and between the molecules or atoms.
In your second question if the temperature is different in two isolated bodies but in contact with one another then energy will flow from one to the other until equilibrium is reached. Energy is always convertible from one form to the another.