Youngest and oldest active player Which currently active player is the youngest and which the oldest ?

Korchnoi is a candidate for the oldest, but I do not know if he is still active.
The answer to your question

Korchnoi is alive. And playing! He played a match against Wolfgang Ulhmann last week (15-16 February 2015) in the Veterans section of the Zürich Chess Challenge. He won two games and lost two.

However, today (22 February 2015) the oldest active GM is the American Arthur B. Bisguier (Elo 2170) born in 1929. Korchnoi was born two years later.

But the most veteran player title is for Lourenço Joao Cordioli (Elo 1928), a Brasilian lawyer born in 1916. And he plays still; he actually got the 100th place in the Floripa Chess Open 2015 on January.

The youngest FIDE rated players are two boys born in 2010, an Indian boy rated 1036 and an Iranian boy rated 1340. I prefer not to give the names to protect their privacy, since they are so young.

The youngest GM is Samuel Sevian (Elo 2531, born in 2000), the youngest USA GM at the age of 13 years, 10 months, 27 days. There are also two WGMs born the same year:
Zhansaya Abdumalik (Elo 2379) from Kazakhstan and Gunay Mammadzada (Elo 2334) from Azerbaijan.

Some details on how I found the information

To answer your question I have used the latest FIDE list of active players of February 12th 2015. But it has been more difficult than expected because of errors and missing data in the list.

For example, there was one player in the list born in 2049?! (maybe 1949?), another one in 205 (2005?), another in 1881 (1981?) and another in 1895 (1985?). Then, quite a lot of players had 0 or 1900 as birth year, which surely means that it is unknown.

And finally, according to the FIDE list there are 1 active player born in 2015 (?!), 3 born in 2014, 5 born in 2013, 3 born in 2012, 19 born in 2011... all of them unrated (of course). I confess I don't know what this means.

Anyway, I started looking for the oldest player. The first serious candidate was Carl Weibrecht (German, born in 1911, no FIDE rating). Although he appears as active in the list, I found a message in the website of Schachkreis Zugspitze dated May 1st 2011 saying 


  "Chess Circle Zugspitze mourns chess friend Carl Weibrecht from
  Garmisch" (Google translated).


So he might not be active, after all...

The second candidate to the oldest player title was Dr. Horst Reichel, professor in Computer Science (also German, born in 1912, no FIDE rating). I have found some of his games for the period 2003-2006, but not later. So I am not sure if he is still playing. However, if the birthdate is correct he played till well passed 90 years old.

Then, there are other apparently active players born in 1915 (all without FIDE rating)... And at this point I decided to restrict the search to rated players and GMs.