The general gist of this epoch is correct as far as we know, but the details are vague. The most likely scenario is that stars will continue to form for billions of years but each generation will have more and more red dwarfs, which will burn steadily but dimly for up to 1 trillion years. Based on this, the last star could form even 100 trillion years from now. But instead of bright galaxies, we would be looking at a large reddish object, peppered with glowing embers slowly dying.
Between 1 million billion and 100 million billion years into the future, stars and planets will either escape galaxies or they will collide and then fall into black holes. Most objects will escape, but up to 10 percent will end up in the black holes.
(So far, if you think this has been easy, then good. Now is when things get complicated.)
Decay, Or Not Decay, That Is The Question
The future of the universe beyond 100 trillion years depends on quantum mechanics and, in particular, if protons decay or not. If protons decay, then all objects in the universe (bar black holes) will crumble. Planets will go first. Heavy elements will break down into lighter and lighter ones until they are hydrogen. The hydrogen will just turn into light and electrons. The same fate will happen to stars. Without proton decay, dark energy will be responsible for breaking down matter in about 100 thousand billion billion years.
Black Holes Rule, But Not Forever
After that, black holes will reign supreme, slowly emitting "black body" radiation, otherwise known as Hawking radiation, until they completely evaporate. At that point, the universe will be in its lowest energy state. The physics get even more nebulous then. Now it just comes down to temperature and entropy. With nothing in it, the universe has reached absolute zero and with no energy available it has reached maximum entropy.
Or, at least the end as far as we can tell. We as humans, and especially physicists, don’t do well with endings. We have invested a lot in understanding the universe, it can’t all be for nothing. And perhaps it isn’t. A few different theories suggest the “dead universe” might generate a new Big Bang. Unfortunately, we wouldn't be there to witness it.