Can a dollar bill be brought into a bathroom?

Tefillin may be brought into a bathroom if they are encased in a double covering. One of the covers cannot be the dedicated tefillin case. Some poskim allow written divrei Torah that do not contain any holy names of Hashem to be brought in with just one cover. Names written in other languages (e.g. on a dollar bill) do not have any kedusha and can even be erased.

ס"ק כד-כה ביאורים ומוספים דרשו, 22-21

Can printed seforim be brought into the bathroom?

The poskim disagree about whether printed sifrei kodesh and divrei Torah must have two coverings in order to be brought into the bathroom or whether one cover would suffice. The poskim say that divrei Torah which are written in a newspaper--whether they are written as a part of an article, advertisement or caption--should not be brought into the bathroom unless they are covered.

ביאורים ומוספים דרשו, 2

May tefillin be worn while walking past a dumpster?

In earlier times, there were areas known as mavo’os metunofos (unclean alleyways). These alleys or streets were filled with filth, and it was forbidden to think Torah thoughts when walking through these areas. The Achronim disagree about whether walking through these streets with uncovered tefillin would be permissible. The stringent view says that they would have to be covered. Contemporary poskim disagree about whether such halachos apply to modern-day streets with garbage dumpsters.

ס"ק כ וביה"ל ואוחזן; ביאורים ומוספים דרשו, 13 ו־1

• One who is wearing tefillin and must tend to his bodily needs must remove his tefillin at least four amos from where he plans on using the facilities.

• A person who needs the bathroom but is worried that his tefillin may be stolen if he leaves them outside may bring them inside if they are covered and tied to his clothing (so that he does not need to hold them).

• According to many Rishonim, a person who just needs to urinate may do so while wearing tefillin if he is not in a beis hakiseh kavua. A minority view is stringent, and one should follow this opinion.

• Is one permitted to sleep while holding tefillin?

• Is one permitted to run a business while wearing tefillin?

• Can tefillin be worn in a cemetery?