No they are not, nor is it even required to be a member of the Church of Jesus Christ of Latter-day Saints. I recently graduated from BYU and knew and worked on campus with persons from other countries and religions as well as LDS persons who never served missions. The Church of Jesus Christ (which owns/operates BYU) does encourage all worthy males over 19 years of age to serve a mission and many do, but most start BYU when they are only 17 or 18 and therefore are not even eligible to go on a mission before their freshman year.
There are three BYU locations. The main school is in Provo, Utah and is simply called BYU. There is also BYU-Idaho in Rexburg and BYU-Hawaii in Laie.
Utah, unless you are talking about BYU Idaho or BYU Hawaii.
Byu Byu
Utah, unless your talking about BYU Idaho or BYU Hawaii
There isn't really a "BYU" alternative. Many who do not get into BYU Provo apply to attend BYU Idaho or BYU Hawaii. Many also apply to attend Utah Valley University (UVU) which is a state school in the same area as BYU.
Byu
BYU no dout
BYU Cougarettes was created in 1946.
BYU Singers was created in 1984.
Tha Byu died in 1840.
Tha Byu was born in 1778.
BYU bands was created in 1900.