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The first confirmed exoplanet is called 51 Pegasi b. It was discovered on October 6th 1995 by Michel Mayor and Didier Queloz. Note: 51 Pegasi or 51 Pegasi a is the parent star.
We won't know that until we are sure that we have discovered all of them.
There have been 95 exoplanets discovered in 2010. You'll need to be more specific on the question.
which exoplanet is 'THE exoplanet'?
The darkest exoplanet is "TRES-2B".
No. An exoplanet is a planet outside of our Solar System.
A few thousand exoplanets have been discovered so far; according to the Wikipedia article on "Exoplanet": "As of 1 March 2017, a total of 3,586 confirmed exoplanets are listed in the Extrasolar Planets Encyclopaedia".The Wikipedia article "List of exoplanets" has a list of such exoplanets.
No one discovered it. It is simply a name given to a duration. 10-24 seconds
51 Pegasi itself isn't an exoplanet, it's a Sun-like Star. But it does have an Exoplanet orbiting it, 51 Pegasi b (informally named Bellerophon.).
No. A moon is not a planet. An exoplanet is aplanet that orbits a star other than the sun.
Both exoplanet and extrasolar planet are planets that are outside the solar sysytem.
No. The nearest exoplanet is more than four light years. We cannot travel anywhere close to that distance