It is permissible and it is not considered as revealing their secrets as the books are widely published.
If the carpets donated as religious endowment (waqf) were many in quantity, such that the mosque does not require them all and are therefore not used, it is permissible to transfer it to another mosque. Otherwise it is not permissible.
As long as the proposed man is religious and virtuous, it is better to accept him for marriage since the encouragement to accept such person is reported in many narrations, although it is permissible to refer to Istikhara.
One must make up the days that he missed after the current month of Ramadan. Furthermore, a sum of 900 grams of wheat, oat, rice or the like must be given to the needy believers for each missed fast, and it is better to give wheat.