Welcome! This sounds very much like my DS-now-8, though his worst period was aged 6 and the descriptions I read about ADHD etc. never did sound like him, so ymmv (always true anyway, of course). He used to get very upset about perceived injustice, had tantrums that he really couldn't control even though he perfectly understood it wasn't acceptable, and had trouble with handwriting and getting stuff onto paper. He also used to be very concerned about following rules, and used to suffer "analysis paralysis" when he wasn't sure what he ought to be doing and so did nothing - which of course was often the worst thing he could have done...
He isn't diagnosed with anything, and his problems were relatively short lived; it was really only that one school year, and since then he's been a model pupil. So there is hope! (Though I don't mean at all to dismiss the possibility of ADHD/PI, and you should certainly go for a full evaluation if you suspect medication might be part of the answer. ASD was something we considered at the time, but it also didn't really fit.)
I really liked the teacher he had that year, but there's no doubt he found her difficult to be with; I think the issue was that she was rather unpredictable, and would be patient up to the point when she lost her temper, which he found hard to adjust to. Fortunately for him, she also really cared about helping him. One thing she did, which might perhaps be relevant if your DD also has the paralysis thing, was to give all the children cards with a green "I'm OK" side and a red "Help!" side, so that if DS was stuck or confused all he had to do was turn his card over and wait for it to be noticed - he found this vastly easier than deciding whether it was OK to go up to the teacher and worry about interrupting etc. This headed off a lot of problems, and also made him know she was on his side.
For writing we've done a bunch of stuff around giving him short, timed periods (e.g. 5 mins) at home to write as much as he can; he's also been helped by a specialist teacher who has taught him some practical tips for writing faster and also boosted his confidence. Again, he's vastly better now than he was.
Good luck!
