Is sin reckoned against a boy who has not reached 15 years of age, and will he be punished for an action he committed at the age of 13, by exposing his private parts to his sister, and will his repentance be accepted?

The child is not held accountable until puberty, as the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane person until he regains his sanity." So, if you allowed your sister to look at your 'awrah before puberty, there is no sin upon you. However, if it was after puberty, then there is sin upon you and upon her if she was an adult, and it is considered a deviation and a regression from natural human disposition (fitra). The door to repentance is open, and its conditions are to cease the sin, regret it, and resolve not to return to it.