Can an aron kodesh be screwed into a wall?

It is forbidden to hang tefillin, whether from the batim or the retzuos, on a peg or nail. Doing so is degrading to the tefillin. Seforim may not be hung either, whether from the pages or the binding. Hanging a bag or container with seforim or tefillin in it is permissible. A Sefer Torah, however, may never be hung, even if it is stored in a bag. Similarly, an aron kodesh should not be screwed into a wall. Instead, it should be placed firmly on the ground or on a platform. 

Should one fast if his tefillin fell on the floor?

In earlier times, it was customary for a person to fast if he dropped his tefillin directly on the floor. The dropping of the tefillin is a sign from Heaven that the person needs to do teshuva. Younger students whose learning would be disturbed by fasting should add to their learning schedule instead of fasting. Older or weak people who have a hard time fasting can fulfill their obligation by giving tzedakah. If tefillin fell while in a case, fasting is not necessary, but it is appropriate to give a small amount of money to tzedakah. One who sees a Sefer Torah fall must fast, even if it fell while it was in its case.

Do tefillin that are stored in their bag need another cover?

In order to protect the sanctity of tefillin or seforim, it is sometimes necessary to cover them with a kis b’soch kis (double covering). Their designated holder is not counted as one of the coverings. Therefore, in situations where two coverings are necessary, tefillin which are stored in their case inside their designated bag must have another covering. The poskim disagree about whether printed seforim also need a double covering.