There is no doubt that an embryo/fetus is a bunch of living cells capable of becoming a fully-grown human being. Bacteria are alive as well. The difference is who controls the destinies of both organisms. Harmful bacteria in a human body need to be eliminated. If a woman feels the embryo/fetus should be eliminated because it is an unwanted invader, then the same should apply. Unhealthy habits can lead to bacterial infections just like sex leads to pregnancy. With so much information and education to be had in today's society, everyone knows how people get sick and how people get pregnant. Just be careful and both won't happen so you won't have to kill unwanted invaders later in the process.
Yes, an embryo is a living thing, because it is a complicated life form that is independent of the mother. An embryo does not start living as soon as it is expelled from the mother. Rather, it is a living, separate thing as soon as it is conceived. For this reason it is fair to give an embryo the status of a living thing as soon as it is conceived.