It sounds like you are putting your feelings about "the school" onto this one teacher. It's only the end of September. I don't know how (unless she was also their teacher in a previous year) she can have yet shown evidence that she chooses the same children for everything.
I feel like, unless something is missing you're being a little unfair. I am guessing that she has started the year picking the "good" students and you have assumed she will continue picking those same ones without waiting to see?
I don't know how she can answer "what is the criteria for being picked and why weren't they picked before?" because it's exceptionally unlikely that there is any specific criteria given. They don't get a certificate after every 17 cartwheels they do. It's likely the teachers are told just to pick a student who stood out to them that week.
She cannot possibly answer why the previous teachers left your child out or always picked the same students because she is not them. She is just a person like anyone else.
I feel like people often assume that teachers personally have a lot more choice and control than they do (assuming they make decisions about homework policies, toilet policies, the curriculum, assessments, authorising absences etc) when in my experience we had very little freedom at all especially later on when academies became a thing. Yet somehow at the same time, often teachers are lumped together as one entity. It's "the school" as a whole that have been leaving your child out after previous years' teachers didn't distribute certificates more evenly.
Even on this one thread there's differences amongst teachers on their attitudes to these things so it's obvious that different teachers are going to do these things in different ways.
Most here have agreed with you that it's not fair to repeatedly pick the same children. I said earlier in the thread that I think it's good to send an email and I stand by that, but I think it's a shame you went at it from an angle of wanting answers for things this teacher didn't have anything to do with and I think it's a shame that you have taken her answer as a cop out.
I'm not sure what else she could have said?
"Oh yes last year in the staff room Ms Miller always spoke about how she felt very strongly that your little Jamie must never get a certificate"?
"Oh yes that Ms Miller is such a bitch. I'm not surprised to hear it. None of us like her."?
"Oh did nobody tell you? To get star of the week you have to wear grey socks on the first Wednesday of the month. You did that? Well then I'd better get in touch with Ms Miller to fix it!"
I completely get that it's horrible seeing your child feeling deflated and looked over repeatedly. But I also think that you should try and open yourself to giving this teacher a chance.
If she does the same as previous teachers did then you can speak with her about it and speak about the effect it's having.