What is the ruling on a woman (29 years old) traveling by plane monthly to Turkey for work without a mahram, knowing that the travel duration does not exceed one week? And is it permissible for the mahram to travel with her merely for escorting her?

Traveling by plane with a mahram is permissible, and it is not obligatory for themahram to stay with you for the entire duration. However, it is necessary to be accompanied by him for both departure and return, due to the generality of the hadith: "A woman should not travel except with a mahram." If you are compelled to work and cannot avoid traveling, and it is not possible for you to find a mahram, then you may follow the opinion of those who permit a woman to travel with a trustworthy company if the journey is for a legitimate need.