The questions you ask suggest to me that you went into this movie with some preconceptions that may have detracted from the experience. You're searching for symbolism, maybe some kind of deeper message. You want to solve the question of the witch, etc. But I think you may have walked in with the desire to decode and analyze everything in what is a relatively straightforward film.
I'm often wrong, but my take on this movie is that it's a simple "spooky movie" where supernatural forces haunt a Puritan family. Where I find this movie shines brilliantly is how the family reacts to this force and to each other.
<spoiler alert>
What do you think would happen if a devoutly religious family has a newborn just vanish? what if you were the one that witnessed it? Or the others who just have to take another's word for it?! Thow in exile and hunger, and the resulting stress would spell disaster for any family.
This movie casts this poor isolated family into the maw of hardship and evil. I was transfixed as everything began to unravel and the family began to destroy itself. The family has a lot of layers, acting in ways that showed their individual quirks and sense of identity. But the focus is on Thomasin. She at the age where she's hits puberty. She's probably confused but the mother mistrusts her and wants to marry her off. And she seems to constantly be in the center of these suspicious, inexplicable events. But as the audience you saw it happen with her! You can't help but be dumbfounded and take Tomasins side. And didn't you groan when she scared the young ones into behaving by saying she's a witch? Sure enough, it comes back to bite at the worst possible time. No matter how much she tries to explain, the truth falls on deaf ears. Thomasin's desperate explaination to her father felt so ...vivid ( Ever tried to convince someone that'll demand answers, but aren't really listening since they've formed their own? ). She's exasperated, angry and diassapointed. Her loved ones are sure she's a witch. They brand and treat her as one even though she's innocent. After they die and her own mother blames and attempts to kill Thomasin, were you surprised when she just gave up and accepted satan in going along? If everyone in your world treats you like evil, at what point do you just say "f-it, I'm might as well live deliciously"?
You just witnessed a beautiful, devout young girl just transform into a witch.