Of course, it is possible. Generally speaking, myopia often happens during teenager, especially school-age. However, after age 40, it is still possible to occur myopia. There are many types of vision problems. First is presbyopia. This is mainly occur in middle-agged, that is, people can not see things which are close. Second is cataracts. This vision problem can cause poor vision, especially in night and patients are sensitive to light. Third is glaucoma. In the later period, patients will lose eyesight. Fourth, vision problem is the most common cause of blindness in people over age 60, that is macular degeneration. Still, there are other vision problems, I just list the common vision problems.
No, it is not possible for you to get nearsightedness from aging. However you may find it difficult to see things near with the aging problem. That is the presbyopia. At the same time, aging problems will make people easily get the cataracts. That is the serious eye problem which you need to pay attention to. You should better protect the eyes carefully when you grow older.