The "common sense" thing is challenge when it comes up with child care help because it's very hard to teach/train it/anticipate everything that might come up, every situation that might arise. We've had similar sorts of things with au pairs (and in fact nannies) before. Sometimes people have their blind spots....I can't say I've never done anything a bit stupid either frankly.
Some of it is a question of growing up a bit and some of it may well be cultural/adjusting to a new environment. The key thing is do they TRY to listen to clear instructions? Do they want advice on how to do things? Or do they get defensive/insist on doing it their way? Do they like your children?
The last bit is really important because if you sense she really cares about your kids, this will help with her risk perception around them. I might do stupid things from time to time as a mum but my kids are my life and I'm always on gaurd and worrying about them. When I have been really concerned about someone's common sense, the key factor I worried about is if I really thought she cared enough to be bothered, if that makes sense. If she's got a really nice rapport with your children it will be salvageable as long as she has a good attitude.
She's not been there long either; give her more time for sure.
The cooking/food safety thing you should be able to train a bit - mention cooking times and also meal plan until she gets a feel for things.
I don't agree that au pairs can't meal plan to the degree of looking in the fridge, picking out a meal, veg, and potato/rice, etc. All of our girls have been bright and absolutely coped with the 'stress' of such a demand. But it does take a bit of time to get a feel for what children like and how to time certain things. If she's making an effort I'd take a deep breath and stick with it.
She also just sounds a bit shy; keep an eye on it but she may also feel exhausted speaking English by the end of the day.