I would agree with Weegle - aupairs are young girls. Think of yourself at 18. They need absolute handholding, or you should assume they do.
Yes, the lack of common sense is not great. But again, I would say just mention it to her. When I was a new mother in hospital, I carried a really hot cup of tea and held it just over my dd. Another mother pointed out that if I splashed, it would get on my dd. That is me at 34 years' old and I like to think I have common sense. I NEVER did that again or anything close.
I have an aupair welcome pack that is packed with information for them from a detailed timetable, local info, to cleaning schedules to houserules. It is a bit OTT but I have about 50+ houserules, with an entire section on child safety including don't leave the children alone in the bath, don't let them go off with another person without checking with me first, put the brakes on the buggy if on a slope, watch them near water ... you geddit. Ok, I don't have the one about not giving boiling water to them ... I went through all the important ones with her on the first few days of 'induction'.
For my first ever aupair, in the month or so before she arrived, I spent it devising the houserules, thinking about how she would fit in, how to settle her in (including making friends and joining English lessons), what a typical day would be like. It was mental preparation for me and an exercise in lowering my expectations. Plus reading mn threads on aupair travails.
It could be that you did the same, and still feel under seige. It's ok, just help your aupair move on to another family sooner rather than later. I would think that families are still just about looking for Oct starts. You can expect demand to start falling off sharply soon after.
Tbh, dh nor I never really had issues with sharing our space with an aupair and dh was the one with concerns about privacy. It does sound like your aupair is doing your head in. I hope you manage to resolve this.