Observing planets around stars other than Sun if very difficult. Figuring out if they have moons will have to wait for some technological advancement.
But judging from our star system they shouldn't be too uncommon. Saying anything other than this is pure speculation.
Agreed that this is all speculation. But based on the solar system, "moons" appear common, but the "Moon" may be uncommon. According to current theory, for our moon to form, there had to be two planets form with orbits stable enough for the planets to form over millions of years, but unstable enough for the planets to eventually collide. How common such a scenario would be is unknown, but at the very least it appeared to only happen once in our Solar System.
While life should be possible without moons, it appears that our Moon greatly accellerated the process of evolution in two ways. First, the collision that formed the moon may have also created the plate tectonics that allows for energy hot spots for new life to use. Also without plate tectonics, all land would have eroded such that the Earth would be covered in water, which while not necessarily harmful to life, is certainly harmful to us. Second, the moon creates tidal pools which allow for different environments which encourages organisms to adopt (evole) to fit the different envirnoments. Thus, tidal pools may have greatly speeded up evolutionary processes.
Probably not. Earth's Moon is unique in the solar system with the possible exception of Pluto's Charon which also was likely formed in an impact event (along with the much smaller Nix and Hydra).
The gas Giants (Jupiter, Saturn, Uranus, and Neptune) all have two types of moons. The "regular" satellites which probably formed more like how the planets formed around the sun, and "irregular" moons that are most likely captured asteroids.
Neptune's Triton may also be a captured dwarf planet.