How would one calculate how far away a point is (latitude/longitude) from the international space station given its latitude/longitude/altitude? The distance would be direct as if drawing a straight line from the two points, even if on the other side of the Earth.
If $r$ is the distance from the Earth's centre, $\phi$ is the longitude in radians (increasing from zero at Greenwich as one goes eastwards) and $\theta$ is the latitude in radians (increasing from zero at the Equator as one goes northwards), then the $(x,y,z)$ coordinates are given by:
$$p(r,\phi, \theta) = r(\cos \phi \cos \theta, \cos \phi \sin \theta, \sin \phi)$$
Given two sets of coordinates $(r_k,\phi_k, \theta_k)$, the distance is given by $\|p(r_1,\phi_1, \theta_1)-p(r_2,\phi_2, \theta_2)\|$.
In your case, we can take $r_1=R$, $r_2=R+A$, where $R$ is the radius of the Earth (I'm assuming a nice sphere, of course) and $A$ is the altitude of the station above the surface of the Earth.