Very interesting. My undergraduate degree is in church music and I am totally unfamiliar with LDS hymnody. What takes place in a sacrament service.
Most Sundays the basic service is the same.
After a welcome from a member of the bishopric (the leader of the congregation and 2 counselors are the bishopric) we sing an opening hymn, followed by a prayer. Then any administrative business (like announcing and sustaining new leaders or other positions). Then a "sacrament hymn" followed by the sacrament, which is passed to the congregation.
After that a series of sermons. We call them "talks." Often a youth age 12-18 speaks, then two adults. Between the two adults might be a choir number, or special music (instrumental or vocal), or a congregational hymn.
The service is wrapped up by the person who gave the welcome, and concluded with a closing hymn and prayer.
Typically lasts about 70 minutes.
There are a few exceptions to this standard. The most frequent is "fast Sunday" which is usually the first Sunday of the month. On that Sunday we fast for two meals and donate the money we would have spent on food. We also forgo the speakers and instead have a testimony meeting. After the sacrament members of the congregation are welcome to testify of their faith. We call it "bearing testimony." On fast Sunday we do not have that "middle" hymn, so you will only see three hymns listed on this thread those weeks.
A couple of other exceptions are "general conference" where the entire church is instructed via satellite, internet, etc by the overall church leadership. That happens twice a year (first Sunday in April and October). Anther exception is "stake conference" where a stake (about 10 or so congregations in the same area) meets to receive instruction from the local stake leaders. This usually happens twice a year, but varies from state to stake as to when. Another exception is "ward conference" which is a special meeting for the individual congregation.
Sometimes there are other special services where the "three talks" don't happen. One would be "primary Sunday" where the children age 3-12 do the service (once a year, usually late in the year). Or youth Sunday where the sermons are all given by the youth age 12-18. Or Christmas Sunday, where the service is mostly music.
One more thing - we have a "block" of meetings that last three hours. The sacrament meeting is only one of them. We also do a Sunday School where we learn in a classroom setting. This year is Old Testament, today for my ward was Hosea.
The third meeting we divide into groups. Men in "priesthood," which is further divided by quorum, so the youth 12-13 are together, 14-15 together, 16-18 together, younger men (typically) together, and older men together. Likewise, the girls 12-13, 14-15, 16-18, and women generally.
The "primary" meets during Sunday school and "third hour." That is kids age 3-12. Nursery is for those 18 months to 3 years. Alas, parents keep those under 18 months with them through the services.
We post our hymnal online here (most of them, anyways - a few are copyrighted). The congregation has hymnals in the pews. This hymnal is under the "hymns" link. There also is a children's song book, also at that link. Play with the links and you can find a player and the words.
I think you will find a strong protestant feel to the hymns, including many borrowed from other faiths.
Hope I helped. Feel free to ask any other questions.