yes
In Michigan, Cassiopeia is a circumpolar constellation: it never sets below the horizon. So, the answer to your question is: "At night." Any night there are clear skies you should be able to see Cassiopeia.
The circumpolar constellations are visible throughout the year from all latitudes on Earth. Examples include Ursa Major, Ursa Minor, Cassiopeia, and Draco. These constellations never set below the horizon, making them visible in both northern and southern hemispheres.
when the sun/moon appears to slowly meet the horizon and disappear
The Big and Little Dippers can be seen usually every night, although are much brighter in the Winter.
The circumpolar constellations, such as Ursa Major (containing the Big Dipper), Cassiopeia, and Draco, never set in the sky over the UK. These constellations are located near the North Celestial Pole, so they appear to constantly circle around the pole without ever disappearing below the horizon.
there are no specific three. The five northern hemisphere ones are Ursa major, Ursa minor, (big bear little bear) Draco the dragon , Cassiopeia and Cepheus. The 3 southern ones are Carina, southern cross, and Centaurus
No, stars do not set below the horizon at the same time each night. The position of stars in the sky changes throughout the year due to Earth's orbit around the Sun, causing them to set at different times each night.
The sun is below the northern horizon at midnight in the Northern Hemisphere.
The western horizon.
That depends where you are on the earth.Seen from the USA, or from anywhere in the mid-latitudes of the northern Hemisphere,Ursa Major, Ursa Minor, (big and little dippers), Cassiopeia, and Draco are always up.The farther north you are, the larger this region is.From the southern Hemisphere, a whole different set of objects (with which I'm totally unfamiliar) is always in the sky. The farther south you are, the larger this region is.Seen from the equator, everything in the sky sets below the horizon every day.
Cassiopeia can be seen from locations around the world within the latitudes of approximately +90° to -20°. The constellation is best visible in the Northern Hemisphere, appearing circumpolar from latitudes above +20°N. The exact longitude for viewing Cassiopeia will depend on local horizon obstructions and light pollution.
Twilight is when the sun is below the horizon- either has not yet risen, or has just set. Civil twilight- what most people mean when they say twilight- the sun is no more than 6 degrees below the horizon. There is also nautical twilight, where the sun can be as much as 12 degrees below the horizon. That time is used by sailors to take "sightings" on stars with a sextant for navigation. In Nautical twilight, you can see stars, but there is still a visible horizon to use in your sightings.