Is it permissible to dedicate oneself to the service of the Messenger and his visitors in Medina, knowing that I am from Palestine and 27 years old?

The questioner's intent regarding "serving the Prophet and his visitors" is unclear. If she means serving the Prophet's Mosque, this is a legitimate act, but it is not suitable for a woman's nature due to the possibility of her mixing with men and being exposed to temptation. A woman must have a mahram (definition) when traveling, based on the Prophet, peace and blessings be upon him, saying: "A woman should not travel except with a mahram." Her staying there without a companion exposes her to dangers. Moreover, some scholars disliked prolonged residence in the Two Holy Sanctuaries (Mecca and Medina) fearing dereliction in their rights. It is advised to abandon this idea and focus on honoring one's parents, as that is better, based on the Prophet, peace and blessings be upon him, saying: "The parent is the best of the gates of Paradise," and his saying: "Stay with her [the mother], for Paradise is at her feet."