Why on earth she is happy with this is beyond me.
Well, because that's probably as much as is sensible to hope for at this stage for the vast majority of children! If someone else can read his writing and understand it without too much effort, if he's using interesting words, if his motor control is good enough that he can write so small, then he's doing OK. In fact, better than OK.
The size thing will probably sort itself out as time goes on. DD also likes to write in really titchy writing but I suspect it's just because she can and I know she can write at a sensible size when she wants to (and I don't bother to make a big deal out of it because, really, she's a bright kid, she won't leave school unable to write). I bet your son can write at a sensible size too, if he wants to. How about a small reward for each page of writing completed at home at a sensible grown up size? As for the spelling, I think it comes with time and reading widely is part of it because your child will unconsciously absorb spellings from seeing them a lot - I would not really be happy that a good reader was on purple level at this stage and would be asking for them to be brought on a bit and given something more challenging because the vocab just isn't wide enough. If the school didn't want to, I'd be asking why not. But if, as you say, your school likes them to read every book in every level then just ignore the school books a bit. Read them on the first day or two after the books are given out and then give him TinTin or Asterix or something fun which plays with language and will give your son something to draw on later on when it really matters. And if they ask why you are ignoring the reading books, well, tell them!
Having said all that, if your son is confident in writing and happy to do it, I wouldn't worry too much. The mechanics of it, including spelling, improve with age and further teaching, which will become more prevalent higher up the school, and it sounds like you will be helping him so he will not leave school unable to spell! It will be OK. The most important thing, IMO, is just to try to foster a love of this kind of activity and to support him in his independent exploration of it as much as you are able.
I do think that possibly selective and non-selective schools approach this from slightly different perspectives, and with good reason, so possibly you need to try and trust the system you've chosen and see how it pans out. You're not going to let him leave school unable to write and the school doesn't want him to either....