As a nanny of many years, both live in and live out, yes please! A list of the random things around the house that may differ or house preferences is great- for example be careful pulling out the washing machine drawer it falls easily, we prefer to use ironing water rather than tap water, general living things. Then anything job specific that may be overlooked when doing introduction to the job, like we prefer to buy only organic meat for the children so it's ok to spend a little more for that, or we prefer to buy all the children's food and leave the house stocked so let us know if you find yourself running out or want to try something new.
A nanny diary is brilliant, when I first start most jobs or if I have a baby or toddler I find myself filling each day with times and sizes of feeds, notes if feeds or naps were different to the norm, and I personally used to note all spends at the bottom so parents could see if they needed to up the money left or if they felt I was spending on things they'd prefer not.
I'd also recommend covering what happens if nanny is unable to go home/bf on a weekend, if this is in contract that they no longer live-in during the weekend fine but if not maybe something about access to kitchen etc if this is limited space, or about noise if coming in really late.
An info list is great for any nanny live in or out, numbers of children's schools, Drs, friends living locally who could help in a true emergency- this massively helped me as I was unable to contact a parent who was out of country so I contacted their friend who had the youngest while I took 3 year old to casualty with a head bump.
The best families I've worked for live-in have been those who allowed me to add food to their shop, cereal they don't have or whatever, and allow some use of nanny budget while eating out and about with the children. The worst one was one who didn't consider an extra adult in the family might just use more food than not so ordered exactly the same food they were used to so it was either a small bowl of terrible muesli or no breakfast or buy me own, and when out even if they told me to take the kids to a place where they ate like a softplay there was no budget for me so either sit eating nothing and have a sad brought from home sandwich alone after the children or buy my own in a place I'd never buy. Think SW London posh kid's places cafe prices.