How wonderful that you have found someone who fits your family so well! Don't let her get away =)
I have done childcare for 15+ years, the last 2, since my son was born, he has come with me. Here are my answers...
1. N/A... except now that I am in school trying to find someone I want to leave my son with I am realizing how difficult it can be to find that right person. If they were a good fit in all those ways you mentioned I wouldn't hesitate for a second to have them bring their kids. If I was unsure about parenting style or attentiveness or general skill with kids, it could be a tipping point away from using them.
2. The other children's care was never compromised, and the alterations to their activities were present, but minimal. I would not take jobs where I could not offer the same quality of care I did before having my son. A few more minutes of waiting for something, or having to share - yes, having their needs or wants ignored or dismissed - no. I would ask about her children's normal routine/naptime. My son did almost all his napping in a carrier for the first year, so he could nap while we were at the park, or playing dollhouse...etc. Find out what her LO's nap routine is and ask how she would manage the 2, as well as get them outside to play.
The only situation I can imagine where she would have to choose between saving children is like a rowboat capsizing... and I don't imagine she'll take the 3 little ones out on a boat herself.
3. We handled sickness exactly the same way I did when I got sick as a kidless nanny - I call the parents, tell them my (or my son's) symptoms and ask if they still want us to come. If their day was flexible or they had something coming up and could find someone else, we stayed home. Most of the time we just resigned ourselves to our families sharing germs. (Which is still way less than a daycare setting).
4. I brought some lunch and maybe a snack, and we would share everything. Feeding preschoolers separate snacks is a recipe for lots of frustration. I knew me and my son were welcome to anything in the kitchen, and that contributed to a really relaxed, enjoyable time. I also fed their daughters plenty of times, but no one was keeping track. Naturally I brought anything else my son needed.
5. I meant to write out a contract, and always encourage it. I have a really informal (we had a mutual friend, now we are good friends) relationship with the main family I worked for/with. I did a kind of verbal contract with her, laying out how we handled sickness. Like a previous poster said, income stability can be rough as a nanny (especially part time for multiple families... eek!) so I said they could drop one day a month w/no pay, 3 w/half pay and I needed the rest that I was expecting for that month. Throughout we were just really straight forward about what we needed for it to work for each of our families. We tried our best to take care of each others needs, and it worked really beautifully. At different times we both initiated a "how is this working for you?" conversation to make sure we were on the same page.
6. First ask her. As a nanny I was a private contractor, I offered my style of childcare and my fees, and if that fit what a family wanted - then great! It is not a nannyshare. Those take into equal consideration the wants and convenience of both families. She is coming to your house, when you want her and working around your child's routine. If you were taking your child to her, and she was bringing her along while she took older kids to activities and ran her errands that would be reasonable. But just like you, she still has all her responsibilities to take care of when she gets home from work. Yes, the lower end of the range is reasonable.
She will be able to sense the attitude you have about payment, so I would urge you to examine what you value and truly think is fair in this situation. I have had people who obviously were trying to figure out how little they could get away with and it feels really bad. I have never been paid the high end of the scale because the families I know and love don't make enough and that was okay. I did charge a bit lower than the going rate when I brought my son. But if I knew you were willing to pay an 18yr old who had done a couple summers of childcare $6/hr more than me, I would be really bothered.
Caring for children is a very strange field because the most important skills are not quantifiable. Does that make them less valuable? I am not saying this all in a critical way, it is something I have tried to sort out in my own head for a while. A few years ago I worked asst managing a food service establishment while nannying part-time. I got paid more at the food-service, but I saw that my unique gifts, and the skills and patience I had developed over the years were used and challenged so much more when I worked with children. So I quit and became a full-time nanny. Then I had a son. If I had stayed in food service, by that time I would have been making enough to pay for childcare and still make some money afterwards. Instead, I was a nanny so I brought him with. None of my talent with children, care or passion for facilitating learning and connection diminished with his birth. Instead it gave opportunity for me to coach respectful and compassionate interactions between the children and for them to develop their closest friendships. So should my pay have been cut in half? No. His needs were added to the equation so my rate was slightly lower than otherwise ($2-3/hr).
Now I don't know your potential nanny. Not everyone is me, or truly values the work and relationships in the same way. But if you have a gut feeling it will be a good relationship, and can work out the logistic, then celebrate and be thankful for this gift!