Check. I despise the giant/dwarf system of stellar nomenclature because it’s so freaking confusing. Particularly when you have a yellow red giant (they do exist), or “It’s a blue giant” – is that a particularly large bright main sequence star, or a very hot red-giant-type star or a blue supergiant?
Not without external forces. Law of Conservation of Angular Momentum. The rotatory force can be transferred to something else (the astrophysics describing this is bizarre, I understand). But it can’t just stop spinning for no apparent reason.
The only thing black, white, and brown dwarfs have in common is their tasteful neutral colors.
A white dwarf is a star that, having burned all its core hydrogen and undergone red-giant-ism and catastrophic collapse, is now composed largely of “degenerate matter” – a rather peculiar term to describe nuclei suspended in an electron fluid, so to speak – something signficantly more collapsible than ordinary matter with electrons in discrete orbitals. It’s a star that collapsed partway and stopped, owing to mass considerations. (We would need to consult one of the SD astronomy professionals, either the werewolf or the Marswoman, to get that explained any clearer, I think.) Typically white dwarfs have masses ranging from a large fraction of a solar mass to something like 2.33 solar mass (Chandrasekhar’s limit, IIRC).
A black dwarf is simply a white dwarf that has been in white dwarf state long enough to have cooled off enough to no longer shine. (White dwarfs shine because they’re white hot. What keeps them white hot for aeons is a matter for our astrophysicists to explain.) As you note, they are theoretical; probably no white dwarf has existed long enough to become one as yet, anywhere in the Universe.
A brown dwarf, on the other hand, is an object composed of the same raw ingredients as a Jovian planet or a star, but in the mass range between Jupiter and the smallest, dimmest, least massive red dwarfs. Between 10 and a few hundred Jupiter masses is the right range: a very small fraction of a solar mass. They glow, dimly, in deep red-brown or purely in the infrared, from heat generated by gravitational collapse – what would serve to heat and compress the core to the point of fusion ignition in a larger red dwarf star, but they’re not massive enough to get the compression or heat necessary.
To be 100% accurate, Jupiter might well be termed the smallest, coldest brown dwarf known, since its frigid “visible surface” temperature, while colder than it ever gets on Earth, is nonetheless 100 K higher than what it ought to be if totally heated by solar radiation.