Frankly, I don't get how the Libertarians support abortion.
The choice argument as put forth by both Libertarians (big-L) and social liberals has a glaring flaw: by choosing to engage in sexual activities that carry the inherent risk of pregnancy, the woman is implicitly choosing to accept that risk. And, as such, if she voluntarily chooses to engage in activities that could potentially lead to pregnancy, she must also simultaneously accept the personal responsibility that is inseparable from her choice. And, if the woman is not of legal age, the responsibility for properly informing the woman, as well as the responsibility for the woman's failures, ought to fall squarely on the heads of her parents or legal guardians.
That said, this argument fails when you consider cases of rape and incest; that's where the waters really are murky.
I think the biggest issue with abortion is the question of whether or not the fetus is living. If alive, no circumstance permits abortion, including cases of rape and incest, unless it threatens the mother’s life.
Not so. You're looking at it from the wrong standpoint. Libertarianism only requires that result if you do not acknowledge the humanity of the unborn child. Libertarianism can be framed in terms of legitimate state use of force -- the state only legitimately uses force to protect its members from force and violence by others. Thus, a state may, and probably must, enact laws prohibiting murder, assault, rape, etc. This is the minimal basis of any society, and only anarchists would argue that a state has no legitimate right to act to prevent the murder of defenseless members.
If the unborn child is a human being, that defenseless human being is entitled to protection by the state since it is incapable of protecting itself from violence by others.
Probably the same way Republicans support abortion.