Is it obligatory to seek permission from parents before entering their room, or is knocking on the door sufficient, especially when there is a need to wake one of them for Fajr prayer?

You must seek permission from family members before entering their private rooms, based on the Almighty’s saying: "O you who have believed, do not enter houses other than your own houses until you ascertain familiarity and greet their people." The only exceptions to this are children and slaves, outside of the three specified times of nakedness. However, once children reach puberty, they must seek permission in all circumstances.

Regarding your entry to your brother's room to wake him for Fajr prayer, there is no harm if he has given you prior permission. However, without prior permission, it is not permissible, as Abdullah ibn Umar said: "A man should seek permission from his father, his mother, his brother, and his sister." This is also supported by sound narrations from the Salaf regarding the obligation of seeking permission from mahrams (unmarriageable kin) to avoid seeing awrat (private parts).

Therefore, seeking permission is obligatory for everyone, even mahrams, to avoid the exposure of awrat. A man must seek permission from his mother, his sister, and his adult sons and daughters.