Energy of a photon I undestand that the energy of a photon is given by $E=h\nu$ where $\nu$ is the frequency of the light. Is this the total energy of the photon? Or its kinetic energy?
 A: Its "kinetic" energy (if you can call it that) is its only energy. It has no mass.
A: It is the total energy of the photon and in some sense it is also the kinetic energy. The energy-momentum relation says that the energy of an object is given by
$$E=\sqrt{(mc^2)^2+(pc)^2}$$
Here $m$ is the rest mass of the particle. When a particle with mass is moving at non-relativistic speeds (it moves much slower than the speed of light) this relation can be approximated as
$$E\approx mc^2+\tfrac 1 2mv^2+\dots$$
The term $\tfrac 1 2mv^2$ comes from $(pc)^2$ so $pc$ can be called "the kinetic energy"$^\dagger$. For photons $m=0$ so the energy-momentum relation reduces to
$$E=pc$$
So for photons the kinetic energy is the total energy. Another reason to motivate this is that photons that climb out of a gravitational well get redshifted, i.e. their frequency becomes lower. Massive particles slow down when they climb out of a gravitational well but photons, which can't be slowed down, become lower in frequency. Like in this picture:

Now one result from quantum mechanics is that energy is related to frequency, $E=h\nu$, and momentum is related to wavelength, $p=\frac h\lambda$. This is true for all particles, not just photons. What is special for photons is that
if you plug these expression in the energy you get $\nu\lambda=c$.
The reason that $E=h\nu$ is often used for photons is because they don't have rest mass so their frequency is one of their defining features. We are also used to measuring the frequency of light. Your eyes are quite good at this. But to reiterate: $E=h\nu$ is true for any particle, but for massive particles you don't normally compute the frequency.
$\dagger$ The actual relativistic kinetic energy is given by $(\gamma-1)mc^2$ as can be seen here. So this statement is only in the loose sense.
Source of picture: https://en.wikipedia.org/wiki/Gravitational_redshift
A: I am not sure it really makes sense to use the term kinetic energy for a photon.
Energy is useful when we talk about energy differences, such as energy before and after a collision.
It makes sense to separate energy into different kinds for a classical massive particle or object. For such a particle, $\Delta E = \sum_i \vec F_i \cdot \vec d + \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$.
For different kinds of forces, there are different potential energies. For example, if you lift an object against gravity, its gravitational potential energy increases. If you separate an electron and proton, their electrical potential energy increases.
Sometimes you see these in disguise, where other terms are used for what is really the same thing. Chemical bonds are based on electromagnetic forces between electrons and nuclei. But we speak of chemical energy instead of electrical potential energy.
When you compress a spring, you stretch chemical bonds between metal atoms. We speak of potential energy stored in the spring, without digging in to identify it as electromagnetic potential energy.
Kinetic energy is the $\frac{1}{2}mv^2$ term. For a particle, this can be made bigger or smaller as the particle speeds up or slows down in response to forces.
The reason energy is useful is conservation. If two particles interact, one may gain energy and the other lose energy so the totals before and after are the same.
Or for a single particle in free fall near Earth, it may gain kinetic energy by losing potential energy.

A photon has energy, but it doesn't respond to forces and doesn't speed up or slow down. So it doesn't make sense to divide energy up into different kinds like this. A photon can't gain or lose one kind of energy at the expense of another. It gains energy when it is created and looses it when absorbed. The amount never changes. A photon just has energy.
A photon can interact with an atom. A photon may be absorbed and disappear while the atom is promoted to an excited state. In this excited state, an electron jumps to a different orbital. On average it is farther from the nucleus and has a different speed.
You might try to say that the atom now has more kinetic and electrical potential energy. But this doesn't really work as cleanly as it does in classical mechanics. Electrons are very light. A classical description of their behavior in an atom does not work. Because of the uncertainty principal, the electron doesn't have an exact position or speed. So you can't say how much is kinetic energy and how much is potential energy. You can only say that the electron gained energy.
Atoms are much heavier, and you can reasonable talk about the position and speed of an atom (though you can't be infinitely precise about it.) You can talk about how much of the photon's energy went into promoting the electron to another orbital, and how much went into the atom's recoil.
So we just talk about the energy of a photon and the energy of an electron in an atom.
