galaxy - Fate of the Spiral Arms of the Milky Way and Andromeda

It indeed appears the Andromeda galaxy (M31) and The Milky Way (MW) are en route to a collision. This will lead to a merger of the two galaxies forming an elliptical galaxy. The flattened disc structure of M31 and MW comes about because their gas dissipated energy but conserved momentum: a disc is the minimum energy state at given angular momentum. The gas in the disc then forms stars, which are more or less on the same orbit as the gas, i.e. circling the respective galaxies. A disc galaxy is dynamically cold, i.e. the speed of the mean motion of the star around the galaxy is much larger than their random motions.

The merger destroys all these structures and replaces them with a much smoother and dynamically hot structure, when the density is roughly constant on (concentric) triaxial ellipsoids. There are several types of stellar orbits in such galaxies, but most important are the so-called box orbits, when the stars oscillate in a large box-like volume and have no preferred mean direction of motion. In the early phases, the elliptical galaxy will have some temporary structures (so-called shells), which are remnants of the merger process itself.

The gas in M31 and MW will most likely be swept into the inner parts of the elliptical where it may form many new stars and contribute to the feeding of the AGN which emerges from the coalescence of the two supermassive black holes of M31 and MW. But energy fed back from the new formed stars via supernovae and stellar winds as well as from the AGN will drive the remaining gas out of the elliptical galaxy, leaving it "red and dead", i.e. without star formation and young blue stars.

The merger of M31 and MW will hardly increase the already neglible rate of stellar collisions. Given the vastness of galaxies compared to the size of stars, such collisions are extremely unlikely. The only places where such collisions occur are the very dense cores of globular clusters.