Question:
Stars move around the galaxy all of their lives… Do they all have the same velocity or do the ones that are closest to the centre of the Galaxy move faster? And the stars with 8 Solar masses that form black holes continue on the same trajectory?
Answer:
Starting at the end: regardless of the evolution of a star and its variations in mass and density, it always remains in the same (approximate) location in relation to the center of the galaxy and with the same velocity. There are only a few exceptions, stars with high "proper motion" that end up making complex trajectories in the galaxy, given enough time, like millions or billions of years.
Stars do not all have the same speed around the center of our Galaxy. Being a spiral galaxy, there is a rotation of all its layers around the center, but this is a "differential" form, that is, it is not like a rigid body (like a top), but more like a cloud of gas (even if with small friction). The central regions run faster, then, up to about 3 kpc, the velocity decreases, then increases again almost without stopping. But each layer has its own velocity. By the way, "almost non-stop" implies that there is matter of unknown origin, because it does not emit radiation or interact significantly with anything, called Dark Matter, which dominates our Galaxy. The representation of velocity as a function of distance from the center of the galaxy is called the "Rotation Curve", in its descriptive form as above.