The answer to your first two questions is both yes and no - and it has less to do with the law and more to do with how people thought about pregnancy. And the shift in thinking was what led to the efforts to ban it.
#"Blocked Menses"
For most of the 18th and 19th centuries, the human body was generally understood to be a carefully balanced system, and an illness or a change in the "natural" state of the body could indicate there was an imbalance. Lara Freidenfelds described pregnancy in colonial and early America as "ambiguous" and that framing is helpful for understanding how someone might respond to a missed period - which may, or may not, indicate an imbalance. (More on the history around a monthly cycle here)
This sentiment - that a healthy body was in balance and a change in health could indicated a need to restore balance - meant that responding to a missed period was a domestic matter handled on a case by case basis, which meant the response was up to the individual (generally speaking, more on how this was different for enslaved women later.) Understanding this helps us understand not just a change in laws around abortion but also a change in the social norms around miscarriage. If a person missed their period for a few months but then it returned in the third month, the gap could have been due to a change in their diet, stress, or other factors or the bleeding the third month could have been a miscarriage. (It's difficult to know the exact number but we know now that upwards of 25% - 50% of pregnancies end in a spontaneous abortion, better known as a miscarriage, within the first 20 weeks.) What this helps us understand is that people who could get pregnant viewed a missed period differently than we do today. We can think of the first few weeks and months following a missed pregnancy a bit like Schrödinger's pregnancy - and the individual who made the call about how to respond to a missed period was the (maybe) pregnant person.
If a woman thought she was experiencing "blocked menses," meaning her body was out of balance, she could restore balance through a medicinal intervention. known as an "emmenagogues." Although there are different theories on how they gained the knowledge, it was no secret among colonial women which herbs could help restore menses and home medical guides routinely included recipes for "bringing on the menses." While there were women who believed that they truly were experiencing a disrupted menstrual cycle, these herbs were known to be and were treated as abortifacients. Leslie Reagan, author of one of the foundational books on the history of abortion in America, "When Abortion Was a Crime," stresses that a person who had sexual intercourse and then experienced a bout of blocked menses likely suspected a pregnancy and not just an illness. But seeking out the solution to a blocked menses was seen as a resolution to an unbalanced body or a way to deal with an unexpected or unwanted pregnancy. There is a whole bunch to be said about what it meant for women who missed a period and wanted to be pregnant, those who were worried about the side effects of abortifacients, and the complexities around bodily autonomy but that's outside the scope of what you're asking.
#"Quickening" At around 20 weeks or so, Schrödinger's pregnancy typically stopped being Schrödinger's pregnancy as a result of an event (or series of events) known as the "quickening." Generally speaking, quickening referred to the moment the pregnant person could feel the fetus moving and was the most common confirmation a person was pregnant. (I'll defer to those who are more familiar with religious history in terms of what it meant for the fetus' status as a person or being.) That said, the sensation could also be seen as another symptom of the same illness that was blocking their menses which meant a person might seek out abortifacients - which were needed in a higher dosage, making them much riskier for the pregnant person - to bring on their menses. At the same time, pregnant people still needed and wanted an abortion, even knowing they were pregnant. This act of seeking out an abortion was, according to Regan, known as "taking the trade," and meant the pregnant person was seeking out a medicinal or chemical abortion from a doctor, apothecary, or healer after they knew they were pregnant. Yet again, there is a whole bunch of to be said about what doctors thought happened to a person when they were pregnant (according to historian Susan Klepp, the word "hysteria" got thrown around a lot) but that also is outside the scope of what you're asking.
Before getting into why laws were passed against abortion, it's necessary to stress that most of the history above applies to white women and free Black women. For enslaved women, the conditions were different. The historical record is fairly limited but in her book, "Killing the Black Body," scholar Dorothy Roberts explored the heart-breaking decisions faced by enslaved people who could get pregnant. Some made the choice to get abortions - or practiced infanticide - as a way to prevent the enslavement of their children. Others used abortion as a way to maintain a sense of control over their own bodies. Enslavers had different approaches to how they dealt with pregnancies including forcing a pregnant enslaved woman to take an abortifacient or limiting the enslaved woman's movements to ensure she carried the pregnancy to term. Whereas white colonial pregnant people had a fair amount of bodily autonomy, enslaved people who could get pregnant had none.
#When Abortion Became Illegal
We'll be posting a detailed look at the laws around abortion in America for a Monday Methods in December so I'm going to give a bit of a truncated version here. The first anti-abortion laws are generally recognized as an 1821 law in Connecticut and an Illinois law in 1827 which classified abortifacients as poisons and outlawed them. The laws did not seek to punish the pregnant people who bought them but rather, those who sold them. And it should be stated plainly that the dosage needed for an abortion later in a pregnancy could be deadly as there was no quality control over production or contents. Some historians view these laws as an attempt to keep abortion safe for women as they did not outlaw or ban plants that had been used for generations to induce an abortion but instead sought to prevent the commercialization of abortifacients and keep it firmly within the domestic sphere; that is, under the control of women and those who cared for women's health, such as midwives and healers. Most of the laws emerged, though, well after the Civil War.
There were instances in early America where someone, almost always a man, was brought up on charges as a result of the end of pregnancy but the cases were very idiosyncratic and highly dependant on local laws and conditions. For example, a case in Maryland in1652 saw a well-connected man brought up charges for forcing a servant who he'd gotten pregnant (the historical record isn't clear if the relationship was consensual, but there was a clear power imbalance) to drink an abortifacient. She almost died and the fetus was delivered stillborn. He wasn't convicted of attempted murder of the fetus but was charged with fornicating and fined; As was the servant - who was whipped. There was another similar case in 1656 - after beating her did not produce the abortion he wanted, a man forced a servant he'd gotten pregnant to drink poison, resulting in a stillbirth. He escaped punishment by marrying her.
But to the larger question of why abortion became illegal, I'm going to rudely punt til the Monday Methods in December as scholars disagree around the reason for the laws and I'm still working on researching the topic. As an example, there are numerous historians who identity an effort by the American Medical Association in the late 1800s to move pregnancy and childbirth away from midwives to under their charge. A group of sociologists see the laws as more about white supremacy and efforts to limit birth rates among Black, Indigenous, Asian, and Hispanic women and protect notions of true "womanhood" among white women. Some historians identify connections between efforts for women's suffrage and laws that restricted their bodily autonomy. To be sure, it's likely a combination of all of the above.