You asked if women go on missions or just the men and how long a mission is:
All worthy young men should serve a mission. By "worthy" I mean that they have to be living the commandments and going to church and have a testimony (a personal witness to share) that the church is true. They are able to go as soon as they turn 19. Most "elders," as we call young male missionaries, go when they are 19. But sometimes people go a little later. Sometimes a young man is not prepared to go when he turns 19 for one reason or another. He may still go as long as he is unmarried and worthy until he is 26. After that he is supposed to work on the mission of finding a wife and being a good husband and father.
Young male missionaries serve for 2 years. So the overwhelming majority of them are between the ages of 19 and 21.
Young women may serve missions if they choose to. It is not expected or required of them like it is the young men. But many young women do serve missions and they have wonderful experiences and can be very powerful missionaries.
Young women are allowed to go on missions when they are 21. They serve 18 month missions. I don't think there is an age limit for young women. They must be unmarried as marriage and family is our most important "mission" in life. We try to keep that priority first.
Most "Sisters" as we call our young women missionaries are 21 and 22 years old. It is very rare to find older sister missionaries. However sometimes older widows will go on missions. My aunt went on a mission to Brazil after her husband passed away. She is so brave!
Older couples can go on missions once their children are on their own and they can afford to give up their jobs and pay for their own mission. They have lots of leeway on how long they serve and where they serve and what kind of mission they serve. They can do service or office work or proselyte or a bunch of other things. Their missions can be as short as a few weeks or as long as 3 years. Typically they are 18 months or 2 years though.
Hope that answered your question. Let me know if you have more.