I'm also a nanny in Glasgow , and I usually charge between £8.50 and £9.50 depending on what is required of me. So, like if you wanted me to take care of the kids, clean the house and do the laundry for the whole family you would be paying more!
I think that 3 and 6 are completely out of order.
1 really depends on how much time she has between working for you and her other job. Frankly if she is having to roll out of bed come straight to you, drop off the kids, go to work, get the kids and then work till midnight, then yeah she needs to be able to get ready at yours.
2, um... yes. Yes you should feed us. A banana, sandwich, or bit of the dinner I just cooked for the children should be mine if I am at yours during meal times.
4, depends on the reason. If it was the only way to settle a ill or upset child then yes, but I'd probably have tried everything else in the book first, and I would of course tell you straight away first thing the next day. And change the bedding.
5, again, would really try to avoid it but if there was literally no other available appointment and I was desperate then yes. It would just have to happen, my health has to come first.
As for overnights, I would expect at least hourly minimum wage (or at least very close to it, say £50 for 7 hours rather than £52.5). I know fine an well I don't get a good night's sleep on overnights because I am so hyper-aware.