I'm very surprised about predicted end of year levels not being level 3 on the basis of what you've said. Lime books, for a start, are usually seen as level 3 equivalent, so this makes the progress in reading look very strange. Is she still reading lime, or is she a 'free reader'?
Writing is a strange one. A level 3 piece of writing will 'flow' more than a level 2 piece. This is mainly due to more advanced sentence structure and use of appropriate connectives rather than 'and' and 'then' all the time. Time connectives like 'just then' and 'at that moment' are useful to create the 'flow'. Use of vocabulary will be appropriate - not too many adjectives stuck together
and more specific words being used when necessary. Full stops and capital letters should be near perfect. As I said before, we have had groups of girls who were using good language in writing in year 1, and were clearly working at a 2c on entry to Y2 but didn't quite reach the level of maturity needed to be a level 3 writer a the end of the year. (When we say 'level 3 writing', we are talking about children writing like 9 year olds after all!)
Children who lack confidence in maths can sometimes convince themselves they 'don't understand', and it's like hitting a brick wall! It might be worth having a quiet word with the teacher (or even dd) about what she's finding difficult. Perhaps looking at it from a different perspective at home may help.
So, yes, I would be worried about lack of progress in reading. If she was reading lime with understanding in Y1, I would expect her to be about 3b at the end of Y2.
As with writing and maths. I would be a bit
but not so worried. I would certainly (nicely!) ask what the teacher feels has led to the lack of progress (because there certainly has been a lack of progress) and what you can do to help. You could mention that you understand from talking to other people, that children are normally expected to make 3 sublevels' progress in Y2 and say you're a bit worried that dd hasn't managed to do so.
At the end of the day, though, she's still doing very well! 