There are different rituals for different prayers and different prayers for different rituals and events. Some prayers are chanted standing, some sitting, some involve bowing to HaShem. Other prayers are associated with different times of day and day of week, whether it's a day for reading from the Torah, or saying good bye to Shabbat (the Sabbath) for the week.
In Hebrew, prayer is called Tefillah. In Yiddish, it's called Davening. Each of the prayers has its own name, the best-know being the Shema prayer.
Hebrew: tefillah. Yiddish: davening.
A Jewish prayer book is called a 'siddur'.
The prayer is called 'the mourner's kaddish'.
Tzitzit.
kaddish
There's no such thing as Jewish prayer beads. Prayer beads are used by Hindus, some Christians, Buddhists, Muslims, Sikhs and Bahai.
It's called a siddur.
It's called a mezuzah.
A Jewish house of prayer is called a synagogue. A Jewish house of Torah-study is called a beit midrash or a Yeshiva. A home where Jews live is simply called "a Jewish house."
A prayer shawl called a Tallith.
There are no beads on a Tallit or Jewish prayer shawl. There are knots and strings called Tzitzit on each corner that represent the 613 commandments found in the Torah.
Jewish prayer is about the same things non-Jewish prayer is about: thankfulness, praise, worship, and requests for health, understanding, peace, and many other things.
The Shema prayer, based on Deuteronomy 6:4, is the central declaration of Jewish belief.