Welcome to Gaia! ::

Dark matter is a mysterious form of matter that we don't know about but we're pretty sure exists.
Based on observations of galaxies and their movements, and matching those against what our models say should be happening, astronomers have come to the conclusion that there must be a lot of matter out there that we can't detect via telescope. It's called "dark matter" because it doesn't give off light, or reflect light, or even really seem to block light.
Current guess come in three types.
The first is that all the matter is random planet-like junk floating in what is called the "halo" of the galaxies. The halo is a roughly spherical region of the same radius of the galaxy that surrounds the galaxy. It doesn't give off light because all the stars are usually concentrated disks so most of the halo doesn't have any stars. But calculations show that there can't be enough of this first kind of matter to make up the full dark matter quota.
The second kind is called "cold" dark matter. This kind is made up of very heavy particles called WIMPs that, for some reason, don't interact with normal particles, hence the name Weakly Interacting Massive Particles.
The third kind is called "hot" dark matter, made of very energetic but small particles like neutrinos. Again, they don't interact much with normal particles.

Dark energy is a mysterious force/energy/pressure that raises the rate of the universe's expansion. We know very, very little about what dark energy may actually be beyond the mathematics. All we know is that because of dark energy, the fate of the universe is not tied at all to the density of matter in the universe.

It doesn't, as far as I know. Antimatter is a quantum phenomenon, the result of extra solutions to Dirac's equation for particle evolution. Dark Energy is a relativistic, cosmological phenomenon, the result of observations of the universe's expansion. I'm pretty sure that there's no connection at all.