Is it permissible for me to pray without a head covering if I fear being discovered, and is prayer valid in the bathroom out of necessity?

The religion of Islam is one of ease, with no burdens except within one's capacity. A Muslim should fear Allah to the best of their ability. If one fears certain harm to themselves, then they must do what repels this compulsion. The fundamental principle is to perform prayer with its conditions and pillars, and what one is unable to do is waived. So, if you are unable to pray except in the bathroom, then pray. If you are unable to cover yourself, there is no sin upon you for what is uncovered out of necessity. If you are unable to stand, then pray sitting. If you are unable to bow and prostrate, then indicate them with gestures. You are permitted to combine prayers when there is a need. It is advised to learn religious rulings from reliable sources and strive to find a way for the rituals of religion to be performed properly.