Act 14: Is Usagi Turning into a Youma? (うさぎが妖魔に?　/ Usagi ga Youma ni?)

4:13 Writing

These four banners are known as "kakizome" (literally first writing). This is
the first calligraphy written in the new year. Auspicious characters are written
that represent the writer's wishes or resolution from the new year.

First Sunrise of the Year, a very popular phrase used on kakizome, this helps
to underline Usagi's "ordinary" nature.

Fortitude and Vigour: that second character can also be read as "makoto".

4:20 What Luna is sitting on...

Luna is sitting on a pair of kagamimochi (mirror rice cake), leaves and a skewer
of dried persimmons. This is a traditional New Years offering, Luna seems to
be taking place of the daidai (a type of bitter orange) that usually goes on top.
This is usually cut and eaten on January 11th. In the show's time, that would be
the next day as its currently January 10th.

4:27 Rei and New Years'

Considering Rei works at a Shinto Shrine, she would have been very busy. 
Most Japanese people visit a Shinto Shrine in the first week of the year.

5:42 Usagi's book reads:

LunaKara

11:21 Ami's Chart

On the far left, she is measuring body temperature.
Top right, she is measuring blood pressure and circulation.
Second down, respiratory rate
Third down, heart rate
Bottom, cardiac output