This snippet from wikipedia sums it up nicely about his age:
The notion of a boy who would never grow up was based on J. M.
Barrie's older brother who died in an ice-skating accident the day
before he turned 14, and thus always stayed a young boy in his
mother's mind. Ironically, the "boy who wouldn't grow up" has appeared
at a variety of ages. In his original appearance in The Little White
Bird he was only seven days old. Although his age is not stated in
Barrie's later play and novel, his characterization is clearly years
older. The book states that he has all of his baby teeth
About the running away part, same source:
Peter does not know his parents. In Kensington Gardens Barrie wrote
that he left them as an infant, and seeing the window closed and a new
baby in the house when he returned, he assumed they no longer wanted
him. In Starcatchers he is said to be an orphan, though his friends
Molly and George discover who his parents are in Rundoon. In Hook,
Peter remembers his parents, specifically his mother, who wanted him
to grow up and go to the best schools in London to become a judge like
his father and have a family of his own. After Peter "ran away" to
Neverland, he returns to find his parents forgot about him and had
another child (the gender of Peter's sibling is revealed to be another
boy in "Peter and Wendy").
