How did Gedolei Yisroel occupy themselves when spending time in the bathroom?

In places where it is forbidden to think about devarim shebekedusha, it is also forbidden to think about dikduk (grammar of Lashon Hakodesh), since thoughts of dikduk would likely call to mind various pesukim. However, it is permissible to contemplate the following concepts: the existence of Hashem, the lowliness of man (for the sake of humility), tikun hamidos, and household expenses (during the week). On Shabbos one may think about architecture and art. Indeed, it is recorded that some gedolei Yisroel read secular books discussing language, philosophy, or science when they were in the bathroom. 

סעיף ב וס"ק ה-ו; ביאורים ומוספים דרשו, 4 ,עם הרחבת המקור

Is one permitted to say the name of Hashem in an unclean place?

In places where it is forbidden to speak about devarim shebekedusha, the prohibition applies to Lashon Hakodesh as well as any other language. Regarding mundane matters, one may speak in any language including -- in cases of great importance -- Lashon Hakodesh. Some are stringent and refrain from speaking in Lashon Hakodesh even about mundane matters, unless the primary language in the region is Lashon Hakodesh. Referring to Hashem is forbidden in any language. Some of the euphemisms to describe Hashem, such as Rachum or Chanun, can be mentioned in an unclean place. Some forbid saying Rachum, and one should be stringent.

סעיף ב וס"ק ט-י; ביאורים ומוספים דרשו, 10-8

May one enter a bathroom immediately after learning a complex Torah idea?

Although it is forbidden to think about Torah in an unclean place, if a Torah thought entered one’s mind in an unclean place, no prohibition has been violated. Nonetheless, it is incumbent on a person to suppress any Torah thoughts which come to mind. One may enter a bathroom immediately after thinking complicated Torah thoughts. Although one should not daven immediately after learning complex Torah, entering a bathroom is not treated as stringently. The poskim explain that the effort to suppress the Torah thoughts would disturb one’s concentration in tefilah. In contrast, seeing the physical walls of the bathroom would serve as a reminder not to continue thinking Torah thoughts.

ס"ק ח; ביאורים ומוספים דרשו, 7

• In earlier times, a bathhouse was divided into three rooms: 1) the outer room--where people were always dressed, 2) the middle room--a dressing room in which some people were dressed and some undressed, and 3) the inner room--the actual bathing room, where everyone was undressed.

• The inner washing room used to be steamy, dirty and smelly. Nowadays, a mikvah room or room containing a bath does not have these characteristics. Some poskim say that these rooms have the status of the middle room. Therefore, one may think Torah thoughts and recite the brocha over tevilah in such rooms.

• Shalom is one of the names of Hakodosh Boruch Hu. Therefore, one may not greet his fellow in an unclean area by using this word. It is also forbidden to greet a person with the word Shalom if he is bareheaded.

• When is it permitted to issue a halachic ruling in a bathroom?

• May one daven near spoiled wine?

• May one daven in front of a sewage pipe?