An Eagle Scout Award looks good on a college application and so helps everywhere it is not required for BYU or any other school.
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.
Muslims are not specifically banned. Disclaimer: I have no connection whatsoever with BYU. BYU does not explicitly require that students be members of the LDS church. They do require that incoming students receive an "ecclesiastical endorsement"; for non-LDS members, this is done by a "religious leader" of the student's choice and basically amounts to said religious leader certifying that the prospective student lives a "chaste and virtuous life" and will abide by the BYU Honor Code and adhere to their dress and grooming standards while enrolled as a student.
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 no dout
Byu
BYU Cougarettes was created in 1946.
BYU Singers was created in 1984.
BYU Adlab was created in 2003.
Tha Byu died in 1840.