What is the ruling on covering the head, and is it permissible for a Muslim woman to uncover her hair if her clothes are modest? And is a woman considered a Muslim if she observes the pillars of Islam but does not cover her head?

A woman must cover her head, and it is forbidden for her to uncover her hair in front of non-mahram men. A woman who uncovers herself does not exit Islam, but she is sinful. Sins do not make their perpetrator an unbeliever unless he deems them permissible, and they are among what has been unanimously agreed upon as forbidden and their ruling has become apparent among Muslims.