I mean, many of those accused of witchcraft were clearly scapegoats of convenience or superstition, but in the same way that there are modern witches, did some men and women genuinely believe they were dabbling in strange powers?
This is an excellent question but getting into the minds of people in the past can be extremely difficult. The answer can be arrived at, to a certain extent, by a mental exercise all of us can engage in. Have you ever wished on a falling star? When blowing our birthday candles? Or when throwing a coin into a wishing well? Have you ever knocked on wood to avoid a bad fate? If the answer is yes to any of these, then you have engaged in attempts to harness supernatural powers that are outside those ordained by any established Christian church.
Are you, then, a witch? You are likely to say no, but the fact that you have appealed to supernatural forces to manipulate your world could be taken by your peers as reason to regard you as a witch. “But these sorts of things are what everyone does!” you may protest. “True,” your prosecutor may respond, “but you have already admitted to engaging in something that is fundamentally witchcraft, so now the only question is whether you should be executed as a witch.”
Key to this is whether you attempted to manipulate the supernatural, outside the bounds of Christian prayer, to hurt other people. The idea that this could occur was a profound fear in premodern times. It was a given that people could use supernatural means to make things happen. Many healers used extraordinary means to help other people. Others used the supernatural to help people to retrieve lost items. Any of these acts could land one in the docket to be examined under the charge of being a witch, but these positive uses of magic and the supernatural were so benevolent, they usually escaped notice and prosecution.
The fear was that people who could call on the supernatural for positive goals could just as easily turn their abilities against people, in anti-social ways. Someone known to have used the supernatural to predict the future, cure aliments, or to achieve other positive ends was a natural subject of suspicion when things seem to go oddly wrong in a community.
Key to the prosecution of “witches” during the European and American witch craze was the question of whether the accused appealed to demons for their power. In a deeply divided spiritual worldview, where the Christian God was pitted against Satan and there was nothing supernatural in between, a core assumption of the prosecutors and a general fear in the populace was that to achieve negative, hurtful results in a magical practice, the practitioner likely turned to the devil or his minions for that act. With this world view, even your knocking on wood could be suspect, but it was likely to be regarded as innocuous since you meant no harm. The practitioner of extra-Christian supernatural manipulation could, nevertheless, be regarded as a witch, an anti-social practitioner of the “dark arts.”
What you are asking, then, is whether any of the American witches regarded themselves to be in league with the devil. The answer is likely to be a broad “no!” Just as you would not draw that conclusion about yourself because you knocked on wood or blew out birthday candles and made a wish (even if that wish was to hurt someone you didn’t like!).
Did any of the American witches regard themselves as gifted when it came to various non-Christian supernatural abilities? Perhaps. This was certainly the case among some of the tens of thousands accused in Europe, but it would be a rare case to find someone who believed in a forged pack with the devil. Indeed, I doubt that if that ever occurred, it was extremely rare – and it may have involved someone who would today be regarded as deranged. Did any of the victims think, then, that they were witches by that definition? Not likely.
This question is hard to answer; R. Hutton in his book The Witch: A History of Fear, from Ancient Times to the Present, which I recommend, basically concludes there was no actual "witchcraft" at all in Europe and US in the Early Modern Period. He doesn't discuss US witches specifically, but goes over the development of the witch stereotype over centuries in Europe, and over key witch trials (and discusses how the concept of witches exists in other cultures).
This seems to be the general opinion of most historians. For example, this article about witches myths plainly states:
Belief 1: Witches were actually witches.
This one is almost entirely a myth.
During the early modern period (1450–1750), approximately 90,000 women and men were accused of witchcraft in Europe, about half of whom were executed. The vast majority of those accused did not identify as witches, while some did come to think, after being tortured, that they may have unknowingly practised witchcraft.
the source: Witchcraft: Fact or Fiction? co-written by /u/drcmillar/
It's very hard to peer into long dead people's minds, it is possible that some people with mental problems actually believed they were witches, but there could be other reasons too. See, for example, this comment by /u/Surprise_Institoris.
Many accusations and confessions were simply outrageous and plain impossible.
The best comparison is Stalin's purges in USSR in 1930's, where various people were accused of being spies, saboteurs, officers planing to overthrow him etc. After various types of torture, many confessed very improbable things and were executed (for example, 80% of army generals are estimated to have been executed).
(edit) similar questions on reddit in the past:
Question that’s related but also kind of not: if an accused witch claimed not to believe in the devil, or that the devil does not exist.. how would that go over? Was that evidence that they were, in fact, corrupted? Is there even a small possibility that such a statement would work remotely in their favor?