Epsilon Eridani b was created in 2000.
If Epsilon Eridani actually exisits, I think the distance is 10.5 light years.
Epsilon Eridani is a galaxy in Halo books but one day somebody might name a planet after it.
Epsilon Eridani B is still unconfirmed, and details about it's size can only be speculative. Based on it's mass being about 1.5 that of Jupiter, it's diameter will be about the same, as gas giants do not increase in diameter with masses <1.6 MJ. Above this value the planet will shrink. So it's fair to say that Epsilon Eridani B will be the same size as Jupiter - give or take. See related question.
The exoplanet Epsilon Eridani b at about 10.3 light years from us.
"The Solar System". Any other system will be identified with the name of the primary star; for example, a hypothetical solar system around Epsilon Eridani would be called "the Epsilon Eridani system". (Epsilon Eridani is a star about 12 LY away which is very similar to our Sun.)
Epsilon Reticuli b was created in 2000.
Epsilon Tauri b was created in 2007.
Epsilon Eridani B is 10.4 light year away. There may be closer planets yet--I just glanced at the first half dozen in the exoplanet catalog. http://www.planetary.org/exoplanets/list.php?exo=Epsilon+Eridani+b CoRoT-Exo-1 B is about 1500 light years away, making it one of the furthest detected so far.
Eridani is a trinary system, three stars. Eridani B is a whit dwarf. A is an orange dwarf, and C is a red dwarf flare star.
There is no star with that name. Many stars have names that start with "Epsilon", followed by the genitive of a constellation, e.g. "Epsilon Cruxis", "Epsilon Geminorum", etc. If its epsilon segin cassiopeia, it is 520L/Y(light years) away from earth.
There is no such thing as an "epsilon star". There are several stars that have "epsilon" in their names; basically one for every constellation, so "Epsilon" followed by the genitive for example, Epsilon Eridani, Epsilon Crucis, Epsilon Canis Maioris, etc.
No. A star's class on the main sequence is ultimately predetermined by its mass, so a star cannot change its position on the main sequence. Epsilon Eridani is about 82% the mass of the sun, which limits it to a lower rate of fusion and thus a lower temperature and luminosity than a G-type star like the sun. Epsilon Eridani's only change in class will come when it leaves the main sequence to become a red giant.