Missionary service iv voluntary. That said, young Men are expected to serve, if they meet worthiness standards, such as morally clean, pay a tithe, believe the church is true, etc. Young women have the option to serve. Young men can serve missions when they are 18 and have graduated high school. That changed 9 years ago. Previously, the age was 19. They serve for two years. Young women can serve at 19. It used to be 21.
They can have contact with their families via Skype or phone calls. Before that change, they could only make contact via email. I went on a mission 40+ years ago to France. Back then, we were only allowed to write letters. The object was not to keep kids from communicating with their families. We were living on a very tight budget. The cost for me to call home could be over $100 for a half hour. Some families could afford it, some could not. It was more fair if none could do it. Now that internet service is ubiquitous, and basically free, it makes sense to allow them to call home
I saw earlier someone asked about who paid missionaries, They pay their own way, if they can afford it. In the US families currently pay $500 a month for a missiobnary, because it is equalized across all the missions. Some missions the cost is way lower, because of the standard of living, and some it is way higher. They started equalizing costs about 30 years ago. I am not sure of the exact date. When I went on a mission in France, it cost around $400 +/-, and I had to manage all of my expenses on that $400.
As for the work, yes, they volunteer to help people. It serves a couple of purposes. First, it breaks up the drudgery of knocking on doors. A lot of areas are doing away with that practice, because it is just not very effective. The main reason is because it allows the, to meet people, in their own environment, and on their level. It helps build trust, so that they might get the chance to teach someone about Jesus and the church.