Kitty- I've had several different ways of doing it. One family gave me a purse with about £40 in didn't expect any receipts, just let them know when it needed topping up. Another asked when I started to see receipts then never actually asked to see them, when I finished I ended chucking a huge bagful! They were pretty bad at keeping it up to date- for example I'd have £30 or whatever for the week then aske me to pick up 3 or 4 bits from dry cleaners at £10 a pop, so I ended up being owed and with nothing for the kids. So as a general rule I'd recomend keeping on top of what the nanny has left and topping up, and not underestimating how much they may spend.
At the moment I use my PAYG Oyster for the school run- would cost me £2.20 for a single without it, £1.30 using Oyster. Its my one though, I just note in the diary I used 1 or 2 buses today and take the money from the kitty.
A decent sized nanny diary is a must for me- boss arrives around five mins after I am supposed to leave so I don't want to spend half an hour explaining the day. Also useful if you can note anything from the weekend- if child seems ill or whatever on Saturday it may slip your mind by Monday, for example. Just let her know what you want noting- previous boss thought I was mad for noting down nappy changes, to others its important. Also good if you note down DCs DOBs, docs name and surgery number, emergency number of someone local who can help if needed etc.
I've never had a family say anything about mobile use before current job- but I was on a contract so used my own minutes and texts for work. When I signed current contract it had a £20 pm phone allowance, which was a nice suprise! I'm still on a contract but I now don't worry about calling home etc so I can save mins for work use, I can pay for the extra calls. Not that there are many needed!
I've always done full-time but never had a job providing three meals a day! I usually eat before work and after, and have lunch there. Can't eat the same as the child because she is weaning and I batchcook and freeze so I have whatever is in the fridge or cupboard. If I fancy something different I pay from my own money or cook enough for the three year old after school and pay from the kitty. But asking if there is something you could add to food delivery like a certain cereal or bread- I had a family who only ate white bread so I requested wholemeal for me (and got the child on it too!).
Other than that- I'd advise being home on time, keeping communicating, talk about stuff thats not just work related. I had a job where boss never asked if I had a good weekend, or anything conversational. I currently have a boss who asks how I am, appologises when late, doesn't expect the earth from me, treats me like a person and I do try to go out my way to do more for them, if that makes sense!
Let nanny know when you can or cannot be contacted, and for what. No good saying 'call em anytime, for any reason!' then get annoyed when she calls for something you see as trivial or when you're in a meeting. I speak from experience!