Actually they had 2 schools in the Anime that were shown. First shown in Episode 9 School of hard Knocks where Ash used Pikachu to beat a Cubone. The second was after Todd's introduction on episode 56 The Ultimate Test, where Ash attends the academy to bypass the need for 8 badges to get into the Pokemon League....Ash fails hard in that episode. XD
As for age, Ash, May, and Dawn were all said to be 10 in the Anime and I believe their game counterparts were said to be 10 as well by general reference to the "You start training Pokemon at the age of ten" thing Pokemon had going.
Black and White were different with their game characters as Gamefreak came out and said the characters were older than in previous games, but how much older they do not say.
Comparing Japanese and American culture since Japanese children are usually given more responsibility and generally are rated on a different level than american's you could say that the MC's for Japan are 10 while the American counterparts (B/W) are 15ish cause that's when general responsibilities for young adults in America are give. (Driving, some jobs, more focus on school/higher education)
