Date: September 06, 2020 01:10PM
To answer some of your questions:
Men go starting at age 18 for two years. Women go starting at 19 for 1.5 years. Missions can be domestic or foreign. If a missionary needs a second language for either a domestic or foreign mission, this is taught at the MTC (Missionary Training Center.) It is a cultural expectation for men to go on a mission. It is not a cultural expectation for the women, although there can sometimes be some peer pressure among the women to go.
Most missions are unpaid, and in fact the missionary pays a substantial amount of money for their mission. For the men, it's in excess of $10,000 for the two years. In some third world countries the church may pay the local missionaries to serve a mission, and in many cases this is considered to be a desirable "job."
Missionary work is six days a week with one "P" (for preparation) day. Preparation day is spent doing laundry, writing or calling home, and perhaps some recreation. Days are long and stretch into the evening hours. They include study time, visiting church members, proselytizing by various means, teaching lessons, performing baptisms (for the men,) and perhaps doing some service. Missionaries have been known to do street contacting, but it depends on the mission president. Missionaries normally do not go home at any point during their missions, and are strongly discouraged from doing so even for family emergencies.
Younger missionaries can still serve missions even if disabled, but may need to be given special assignments, often living at home. As for "problem cases," it depends on the ward's bishop, who must sign off on each missionary prospect. A bishop can deny a young person a mission, or conversely, send the the young person, hoping a mission will shape him or her up. There are many stories of experienced missionaries "babysitting" a dysfunctional missionary companion.
Senior couples can serve missions as well. They can choose from a variety of assignments and locations, but they pay for their missions, and the cost can be steep. I believe that senior missions range from six months to two years. Some seniors serve multiple missions.
The stated purpose of missions is to convert people to Mormonism, but as others have noted, there is a suspicion that the real purpose of a mission is to bind young people to the church, making them unquestioning, lifelong members.