"A Head Boy یا Head Girl is a Seventh سال student who has authority over prefects and students at Hogwarts School of Witchcraft and Wizardry. They wear a badge.
"At the beginning of the school سال the Headmaster appoints, new prefects as well as one Head Boy and one Head Girl from all of the seventh-year students. On the Hogwarts Express, the Head Boy یا Head Girl of their house has to go through all the things that is needed to know to be a prefect. Most Head Boys and Head Girls were once prefects, although that is not a necessity; one example being James Potter, who was Head Boy despite not being a prefect.
"The trophy room contained a فہرست of Head Boys (and presumably Head Girls). The Head Boy and Head Girl are in charge of the prefects and should be an example to the other students. Head Boys and Girls also had the special privilege of being able to use the Prefect's Bathroom.
"Known Head Boys and Girls
Albus Dumbledore (1898-99)
Tom Marvolo Riddle (1944-45)
James Potter (1977-78)
Lily Evans (1977-78)
Bill Weasley (1988-89)"
from: Harry Potter Wiki
link i believe they still have the same common room and dormitories as the rest of their houses. and yes, they can definitely take away points; not sure if they can award them.
hope this helps! n_n