I was wondering how long sperm can live outside the body? If semen gets on hands or a finger, then is immediately inserted into the vagina, could she get pregnant, or would the sperm die when in contact with the air?

"The life span of sperm after ejaculation depends on the environmental conditions. Sperm ejaculated into a woman's vagina can live in a woman's reproductive tract for up to five days or perhaps even longer. Fertilization is possible as long as the sperm remain alive. Sperm ejaculated outside the body may survive only minutes to a few hours."

Sperm: How long do they live after ejaculation? - MayoClinic.com

It is not common, but yes, a woman could become pregnant that way if she is close to ovulation. Without the right conditions, as it is at other times of a woman's cycle other than near ovulation, sperm will not live long at all.