1a Girl in Gatehaed can't be found ???????
5a Female writer's at a nusing centre for pilgrims ??????
9a Student group pens cryptic clue for 'core' ???????
10 a Opens roll of cloth in sun stupidly ???????
as answered by DannyK and sandyroe earlier.
Fatima.
Female= F, writer's = im which is at centre of at a.
and Fatima is a place of pilgrimage in Portugal