Used to work as a teacher for kids this age: Her attitude is rotten. Yes, his accidents need to be addressed, especially if he’s potty trained and they’re occurring seemingly out of nowhere. However, he could just be so absorbed in what he’s doing, he forgets. Hardly the first child to do so, so 2 accidents wouldn’t have me hitting the roof.
As for the hitting incident, for the first child to hit means that the teacher was probably not paying adequate attention. For your child to have time to react & hit back, it definitely means she wasn’t paying close enough attention. Yes, things happen, but that’s why there’s supposed to be more than one adult in the room. In Ireland, at this age, it’s 1 adult to 11 children, so if the class is a standard 22, there should be a minimum of 2 adults. Ask for a copy of their policies on this. Ultimately however, it was a random incident, or she wasn’t paying close enough attention.
Again, screaming when he’s frustrated, while unpleasant, is not uncommon for a child his age. Screaming, tantrums, etc are commonplace for a nursery, and frankly, if she can’t deal with it properly herself, then she’s in the wrong job. It sounds like it’s being managed at home, which further adds to that.
I would however give her a break on his age. It’s more than likely there’s ages in that class ranging from 2.5 - 5 (maybe not, but I know in my class a few times, we had that range due to language barriers, additional needs, etc). So getting it wrong is fair enough - though the acting as though you’ve gotten your own child’s age wrong is bizarre.
Ultimately, if you’re not happy with the level of care your son is receiving, you have every right to address this. I have seen firsthand that some teachers just do not have the patience for children at all, especially not children who don’t just put their heads down and stay quiet.
ETA: I’ve seen fully grown trained adults who CHOSE to become teachers be outright hostile to children as young as 2-3 because they “didn’t like them” or the child was “difficult.” So I fully believe you OP if you feel this teacher is singling your son out, because it IS possible.