Is it permissible for a person to punish themselves by hitting, and is it permissible for a friend to hit herself as a punishment for her friend's failure to adhere to acts of worship?

Your friend is not permitted to harm herself by hitting herself when you fall short, for the Prophet, peace and blessings be upon him, said: "There shall be no harm or reciprocating harm." Competition in obedience is commendable, but it is better for the deed to be a secret between the servant and his Lord, as it is more conducive to sincerity.