I posted a month ago about my trip to Europe with my 20 year old daughter. I have finally moved out of my home which I have sold to finance this trip

. We will be leaving the last week of March and she will be with me for 3 weeks. After that I plan to stay on in Italy (Siena?) for a time to be determined once I'm there.I will ask my questions as they come up, beginning with the beginning. First off. My daughter wants to see Paris, Rome,Florence, London in that order of importance. Do you think it would be best(cheapest to fly) to begin in London, then to Paris, then to Florence/Rome, where she will fly out of Rome back to the US?
Question #2 What is the best way to get to Paris from London if that is the best plan?
Question #3 Best way to get from Paris to Florence?
Question #4 I think it would be fun to drive from Florence to Rome, and take our time. I would like to stay in Siena for the extended time and bounce around from there. Ending in Rome where she flys out of. What do you think of this idea?
Question #5 I need a cheap extended stay in or near Siena. I have read a lot of the info. here but wonder if there is ever a room for rent in a private home? How do I find out that kind of rental info? My hope is to find an inexpensive way to stay as long as I can. Luxury is not an option!
Looking forward to your input. And thank you for this great website, I love it.
Cherry