What good would the witches plan of becoming immune, Specifically, to fire do them? burning them to kill them is a slow but effective way but you could do it hundreds of other ways, as shown in the movie, they never mention any other actual benefits to the plan.
It could be because fire is the most DEFINITE way to down a witch. The average person isn't going to have the type of weaponry that Hansel and Gretel have. What will they have when encountering a witch, though? A gun or two- which are literal hit and miss- and fire. Fire is something even a NOVICE can use to kill a witch with. A CHILD could kill a witch if given the chance to set her on fire. They're trying to take out their kryptonite.
Barring middle ages paranoia how can anyone mistake a woman for an Dark Witch? this is a world where witches exist and if they do use black magicks they look very, veryObviously Evil, I'd have understood if it was a woman with a bad case of dental hygiene and a serious case eczema or psoriasis, but the woman shown accused even though they are right she is a witch just not evil. is a very attractive healthy looking woman.
It could be they thought of her as a "beginning" dark witch. No obvious rot yet. Mina is a White Witch, so she probably has a reputation of being "odd"/knowing "odd things" as a part of her magic. Like usually seen in works like this, the benign healer/medicine woman is confused for a witch because people see a woman getting inventive with things and immediately conclude "Witchcraft!". The difference is that in THIS world, they have more justification than usual to be suspicious of the odd duck in the populace; who also has a very obvious theme color to her while everyone else is in "nondescript farming peasant" garb. So she makes a convenient scapegoat.