The Megillah (scroll) of Esther is read on the Jewish holiday of Purim. It is read twice, once in the evening immediately following sunset and once in the morning as part of the morning services.
megilat Ruth
You can read the Megillah online on various Jewish websites, such as Chabad.org, Sefaria.org, or MyJewishLearning.com. Many synagogues also livestream their Megillah readings during the holiday of Purim.
It's an Aramaic prayer/poem we read before reading the Torah.
Shavuot is a Jewish religious holiday.
On Shavuot the custom is to stay up all night studying Torah to mark the date that God gave the Ten Commandments. We pray and read the Torah (Exodus 19-20), and eating dairy foods is customary.
The Shavuot celebration originated in Israel and they celebrate a feast.
Haman is mentioned 36 times in the megillah.
No. Tefillin are not worn on holidays, including Shavuot, or on the Sabbath.
Shavuot (mistranslated as Pentecost) was fifty days after the Passover. Still is.
You can buy a copy of a megillah in most Jewish book stores or you can purchase one on the internet.
No. Anything dairy is traditional on Shavuot, especially blintzes.
Shavuot is recognized as a festival by all branches of Judaism, Orthodox, Reform, Conserviative. However, of the three pilgrimage festivals, it is the most frequently ignored. (Despite the good food, since cheesecake is a traditioinal food for Shavuot.) I have been to Orthodox synagogues where hardly anyone showed up for Shavuot, and I have been to Reform synagogues that were crowded on Shavuot. Even so it is probable that more Orthodox Jews take Shavuot seriously.
Yes, Shavuot is a Jewish holy day/festival (Leviticus ch.23).