I know that usually universities only take a certain number of people from the same school, but I was wondering if they would do the same sort of thing for families. For example, I would like to apply to Brown in the fall, but my cousin plans to as well. Would that possibly hurt my chances of getting in?
No it won’t.
It will not. How would they even know it is your cousin? Your first sentence is also incorrect
Agree with the above – colleges do not have quotas by HS.
Even if they learn you two are cousins, you’ll each be reviewed on your own merits. Worry about your own app.