You will probably get a lot of different questions from a lot of different people on this. For what it's worth, here is my two cents. I will try to be as factual as possible, with as little personal opinion.

Yes, BYU sports teams do not play on Sundays. It creates unique challenges, including the NCAA having to bracket us into ncaa tournament regions that play Thurs/Sat in march madness. A part of the reason we have had conference affiliation issues is because of the no Sunday play rule. In the MWC, as a main team, we could kind of dictate that and in the WCC now with mostly religious schools it isn't overly challenging. It is a bit of a challenge with the NCAA, but fortunately they are open enough to accommodate it for the most part.

Yes, the rule is mostly based on religious convictions regarding sabbath worship. As the school is owned by the church and completely oversees all operations, they strive to maintain it's religious standards as closely as possible. Are we perfect? Of course not. Do all students keep the standards perfectly? Absolutely not. But, the school strives hard to keep to the churches standards as much as possible. This is also the reason for the honor code, which requires students to commit to not drinking alcohol, abstaining from pre-marital sex, and other things that are church standards.

For mormons in the NFL, or in any profession where they are required to work Sunday's, it's up to the individual to decide what the feel they need to do for their family. Our religion focuses, almost above all else, on supporting your family and protecting them. So for guys in the NFL, or working on Sunday's, it's really a personal decision on what is best for them and their family.

Hope that helps.