What is known about the way 'dark matter' is distributed? Is it
possible there are dark matter equivalents to conventional atoms? Is
it possible there are dark matter planets orbiting dark matter stars?
If so, could there be some 'beings' made of dark matter, living on the
'planets'?

Buffycat,
Scientists have suppsedly found some characteristics of darl matter.
They took 70,000 measurements of distant dwarf galaxies using the
high-power VLT (Very Large Telescope) and then created a computer
model of the galaxies. From what they suggest I dont think there could
be beings of dark matter. It is distributed throughout the universe
and one article said that dark matter and dark energy make up 96% of
the universe. The main evidence for dark matter is its gravitational
pull on planets and stars, which prevents the planets and stars from
flying out of their orbits. They used computer models to weigh how
much dark matter would be needed. In the models they created, using
their measurements, they discovered that dark matter can only be found
in massive clumps, and is never in a clump under 1000 light years.
Therefore the individual particles move incredibly fast, 9 kilometres
per second. This means that they must be very hot to have the energy
for this movement, being 10,000 degrees centigrade. This is baffeling
because usually hot things would emit light, but dark matter doesn't.

This can all be verified here:
http://www.abc.net.au/science/news/stories/s1567144.htm

and supplimented here:
http://www.daviddarling.info/encyclopedia/D/darkmat.html

There are a number of different dark matter theories, but essentialy
they break down into two groups.  The first group say the dark matter
is just ordinary matter that we can't see, things like small very dim
stars that don't give off enough light to be visible - there's no such
thing as a "dark matter atom" in there.  The other group says that
dark matter is exotic particles and isn't made up of atoms at all (or
even the particles that atoms are made of), so no dark matter atoms
there either.

There's no reason why the universe's missing mass can't be made up of
ordinary matter that we just haven't found as well as exotic
particles, but right now it looks like most of it is in the form of
exotic particles.

Ian G.

If the M-theory is correct, then he dark matter might be normal,
baryonic matter distributed on another brane just like matter on our
own brane. The gravity then "leaks" through to our brane, which gives
evidence of this dark matter. An yes, there will be dark matr beings
(assuming life developed there) on dark matter planets.