Do they allow religious texts in mental hospitals?

yes they often have different religious material in mental hospitals. They even have groups that tell the importance of religion and spirituality. They actually encourage religious involvement in mental health recovery.

Yes they do. Our constitution guarantees us the right to freely practice whatever religion we choose. It also guarantees the freedom from religion if we so choose. By law, they should allow you to bring in whatever religious texts you choose. Also, you have freedom from receiving any religious services that you do not want: like Alcoholics Anonymous for example. (It has been declared a religion by numerous appellete courts).

As long as they don't pose a danger to the patient, yes, they are allowed. Only way it would be banned is if the "religion" told them to hurt others/themselves for some reason.