What I would like to know; -What are the criterions for being allowed into the Citadel for maester education? Could a dwarf in his late twenties like Tyrion be allowed in?
You'll learn more about the Citadel in future books.
In brief, however, there's no age requirement... nor any other sort of requirement, actually. The Citadel is very loosely structured, and open to all. That doesn't mean that all become maesters, however. Oldtown is full of aging novices and acolytes who have never finished forging their chain (or in some cases, never begun)... the Seven Kingdoms equivilent to the eternal grad student of our world.