It's not a cape, it's a prayershawl.
Yarmulkes
The earlocks worn by some very Orthodox and most Hasidic Jews are called payot in Hebrew and payes in Yiddish. There are many variations in spelling.
A Yakama is a piece of headgear that is worn by orthodox Jews. It is a cap that sits on top of the head. It is meant to remind them that God is above them.
Orthodox/traditional Jews wear yarmulkes (kippot) (or otherwise cover their heads) at all times as a show of respect to G-d. Tallit (prayer shawls) are traditionally only worn during morning prayers or at services. There are some holidays on which Jews may wear (or not wear) certain garments worn during certain holidays (e.g., it is traditional to wear white, but no leather, on Yom Kippur).
Orthodox Jewish men wear the Yarmulke all the time. Other Jews (male and female) decide for themselves whether or not to wear it.
Purple during holy week, and then white on Resurrection Sunday (Easter Day).
The pope's ordinary dress (also called house dress), which is worn for daily use outside of liturgical functions, consists of a white simar, a cassock with a shoulder cape attached to it.
the name of a short cape worn in ancient Greece is called a chlamys.
Clothing styles have changed completely more than once. Today's suit did not exist seven or eight centuries ago. In the time of the Sages 15 centuries ago, most Jews wore white flowing garments. Sandals were worn in the non-rainy months. Pants were worn under one's robes if at all. Inexpensive garments were often made of hemp. The one thing that is unchanged is that religious Jews have always kept their bodies fully clothed; thighs and torso especially, both men and women.
Depends on the church. In Greek Orthodox Catholc church, nothing is worn. In the LDS church, a pure white suit is worn, and the person is completely immersed in a tub of water. In my church - Presbyterian - anything can be worn, most likely nice clothes, as the water is just a few drop on the head.
No no no no no no no no
Jews call it a Kippah (in Hebrew) or a Yarmulka (in Yiddish). It is a head covering worn by Jews during prayer and study. Orthodox men wear them all the time. Non-Orthodox men and women wear them only during study or prayer. It is a custom with the force of a law, and although the actual origin is vague, it has come to represent a reminder of G-d's presence.