I used to do £50 for an overnight stay - but that was on the basis (i) that our nanny has no real say in it (this was explained when she took the job that sometimes it would all go a bit pear shaped, and if so she would have to help pick up the slack); and (ii) it was for 2 DCs under 5 so there was a fair likelihood of having to deal with nocturnal wanderings/glass of water/wet bed etc.
Re food, I always say that our nanny can eat absolutely anything but I will point out if I have specific plans for it. It more often works the other way, with post it notes with skull and crossbones drawn by the children saying "Dad - do NOT touch". I do a weekly shop by internet, so tell her to write down what she needs for the DCs and anything she likes - I have never had a nanny take the piss with this.
Re going out - mine does this a reasonable amount, with my blessing. I think it is nice for the DCs to eat out, but we have lots of fairly cheap options - only local Asian/ noodle/sushi/pizza places. Also I am an inveterate "stopper for a coffee", so can't raise an eyebrow at that. My nanny does, however, always prepare and take juice and snacks for cinema, theatre, softplay and meets other nannies for picnics quite a lot, so it all comes out in the wash.
Re naps - wouldn't have a problem with that if everything else was done, children were happy etc - I've always given my nannies quite a lot of autonomy. Would be v jealous though!