6. I know, having read the rest of the story, that what Eleanor wants to go to the school office about is to see if she can get into the running club. I don’t think there’s any need for the mystery around this – when asked about whether she’s ship or silver, you could bring in the thought that her real talent is running, but that Marlington show no interest in sporting prowess in their admissions process – only whether you’re academically gifted or had parents with money. But perhaps one of the prefects who’d shown her around had mentioned all the clubs you could be in, including the running club – she’d go straight to the office to sign up for that, then she’d show them what she was good at.
7. You mention that she took the entrance exam but failed. Perhaps she took the entrance exam back in the summer with the plan that she’d start in September, at the beginning of year 10, failed, had a ‘stay of execution’ from having to move to Marlington from her old school, but then her stepdad had persuaded her mum to send her anyway, after Christmas. There’s also then the sense that she’s a late arrival at the school, so even more of a fish out of water, where other newbies in year 10 started back in September (and incidentally took all the spare places in the running club, as she’ll discover later).
8. I think you could also bring in a little bit about her friends from her old school when you mention the messages on her phone - heightening the sense of having been pulled out of the familiar friendly place to this new, strange school.
9. If you want to lose some detail, I would perhaps leave out the OPES inspectors. Do they have any function in the story at this stage? Could they turn up later?
10. I do think you’re right not to put the bit about Eleanor seeing her own double in this chapter, unless of course she catches a glimpse out of the window of the back view of a girl who looks remarkably like herself (same colour and length of hair) - perhaps spying on the prefects who are spying on the police. Of course, that girl will be in an ordinary, non-prefect blazer, so she will be in trouble for being out of class. You could perhaps then plant the seed for the reader that perhaps she's seeing her future self, without actually confirming that or making it too obvious that she is.
I hope you don’t mind all these radical suggestions. Of course it’s your story, not mine and I realise they’ll affect more than just your first chapter, but I think that making this Eleanor’s very first day, will automatically help to make your readers feel more invested in her – after all, we’ve all had experiences of first days in a strange new school or job, and if this new school feels like an immediately creepy as well as aloof place, all the better.