Remember the CMB light originated everywhere. So there will always be a distance such that light originating from that distance is just reaching us now. Cosmic expansion doesn't come into play here.

> The Andromeda galaxy is expected to collide with the Milky Way in approximately 4.5 billion years. Does this time take into account the expansion of space in between the two galaxies?

Space expanding doesn't physically do anything. It's just a convention that's useful in some contexts. (It represents a choice of coordinates on spacetime.)

Since the misconceived reification of expanding space is pretty deeply ingrained in the public consciousness, here are some articles discussing the point further.

(1) A diatribe on expanding space. This is pretty technical, but it's the most direct attack on the idea of expanding space. One key quote is that

> there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost.

For example, the Milky Way-Andromeda system is no longer expanding, so cosmic expansion is simply no longer relevant to it.

(2) The kinematic origin of the cosmological redshift. Very well written and less technical, although there are mathematical arguments. The main point of this article is that the cosmological redshift -- often framed as a consequence of space expanding -- is more precisely viewed as just a Doppler shift.

(3) On The Relativity of Redshifts: Does Space Really "Expand"? The least technical of the batch. This article is also focused on the interpretation of the cosmological redshift. It includes the choice paragraph:

> While it may seem that railing against the concept of expanding space is somewhat petty, it is actually important to set the scene straight, especially for novices in cosmology. One of the important aspects in growing as a physicist is to develop an intuition, an intuition that can guide you on what to expect from the complex equation under your fingers. But if you assuming that expanding space is something physical, something like a river carrying distant observers along as the universe expands, the consequence of this when considering the motions of objects in the universe will lead to radically incorrect results.

Expansion is a big factor but you can think of the light of the CMB as having originated from everywhere. The part of the CMB we observe is a growing bubble. The light is traveling uninterrupted after having been emitted in the early universe.

To the second question, the expansion of space is not that significant between nearby galaxies.

On average, yes, but in reality the recession velocity is neither constant nor linear. Points at the distance of the CMB scattering surface are currently receding from us at more than three times the speed of light.

The Milky Way-Andromeda system is bound together by gravity, and so is unaffected by expansion. Newtonian mechanics is all you need to calculate the time until the two galaxies collide (notwithstanding the uncertainty in the current distance and relative velocity of Andromeda).