Is it permissible for a girl to correspond with a sheikh to ask for prayers?

There is no harm for a woman to correspond with a scholar to request supplication. A woman's conversation with men is permissible when there is a need, provided there is no suspicion or softness in speech, and no fear of temptation. Correspondence is even more permissible. Evidence for this includes the correspondence between Mu'awiyah and Aisha, may Allah be pleased with them both.