Do the stars in a galaxy have a thermal kinetic energy distribution? I think, there is practically everything given to that: many point-like masses, able to exchange energy pseudo-randomly, and far long enough time to reach a thermodynamical equilibrium.
Of course, the large-scale distribution behavior shouldn't calculated here.
Can we consider the galaxies as rotating gas disks, where the atoms of the gas are stars?
 A: If you're interested in the dynamics of stars in a disk, or any other configuration, the equation you want is the collisionless Boltzmann equation. It also applies to the dynamics of dark matter or other "collisionless fluids". Galaxies typically also have a gas component (which is sometimes in a disk), which should be modelled using the usual hydrodynamics.
A "gas" of stars cannot be modelled as a normal fluid because the cross section for collisions between stars is vanishingly small - for instance if you take two star clusters and put them on a collision course, none of the stars really collide and the two clusters pass through each other, probably deforming a bit in the process. This is in contrast to putting two clouds of gas on a collision course - they will decidedly not pass through each other.
This is the collisionless Boltzmann equation (one of the many possible choices of variables and coordinate systems):
$$\frac{\partial f}{\partial t} + \dot{\mathbf{q}}\cdot\frac{\partial f}{\partial \mathbf{q}} + \dot{\mathbf{p}}\cdot\frac{\partial f}{\partial \mathbf{p}} = 0$$
$f=f(\mathbf{q},\mathbf{p},t)$ is called the distribution function, and describes the probability that a particle (in this context, a star) is found at phase space coordinates $(\mathbf{q},\mathbf{p})$ at time $t$. One interesting property of systems described by this equation is that their phase space density is conserved.
This web page, despite some crappy formatting, gives a nice bit of additional detail.
This book is the canonical reference on this topic in the context of astrophysics.
