Teacher here-
AFAIK there is a cost to screen for dyslexia and sometimes there isn't enough in the school budget to "justify" it. When there is a diagnosis there isn't a whole lot of extra support as most of it can be done with or without a diagnosis. I have a little girl who I suspect is dyslexic but all strategies I'm using I'd use if she did have a diagnosis. It's a tough one but perhaps have a chat with the SENCo if you haven't already? If you're willing to I think you can pay for the screening.
Have the school done an informal screening for it? If so, what was the result of it?
As for the teacher query, raise it with him when your child isn't there tomorrow. Just be completely honest and say how you're pleased she has him as you've heard glowing reports from prev parents (if you do feel this!) but go on to describe how she's doing. It'd break my heart if your child was in my class and they, or you, were feeling like this. We're all here for the same reason so transparency is key. Talk about how you're concerned and ask if they have any resources that could support her at home? Discuss how you've noticed a decline in her MH since start of the year and would like to get to the bottom with it. Is your child usually well behaved and therefore been placed next to a "naughty" child to set a positive example but instead they're being mean and causing problems? Could be a number of things really.
If he responds badly, or you'd like to raise it more formally, speak to SLT.
As for handwriting and spelling, do not worry. As a Y4 teacher I'd recommend practising her high frequency words and perhaps make these fun into games, and another thing I tend to do is get them to practise their handwriting by writing their spellings. Hitting two birds with one stone!
DMs open if you need anything, best of luck x