Consider the following when contemplating taking a baby: it's a wonderful but LONG tour day. Ours lasted about 13+ hours. Plus, the drive between sites is also LONG - 2-3 hours. Baby-friendly? Obviously, that depends on your baby and his/her temperament (and consider there is a tour guide on board who narrates continuously) . And because a bus is even closer seating than an airplane (with no restrooms), consider whether you want to do all that is necessary to care for your baby in very close quarters. Likewise, to get to Windsor Castle from where the bus stops is a pretty good walk. And to get to and through the various parts of Windsor Castle and the Roman Baths are rather steep inclines and steps. Not even stroller-friendly.

Yes there is luggage storage that you access from the side of the bus that you can put large suitcases. On the tour that I went on there was one couple who took their luggage from London with them on the bus because they wanted to stay in Bath for a couple days. I this this company uses coach buses so they should all have storage on the side of the bus.

No

We bought sandwiches and snacks at a restaurant outside of the exit at Windsor (it was really good! Don't remember the name but it was kind of early in the morning and the guy was so nice about letting us order and take food to go. It was down the street which was across from the only exit from Windsor, all the way down on the left.) We visited the queen's grave and then still had time to walk through the apartments and then got out before the gates closed for the changing of the guard AND still got food. You just have to have a plan, which basically means listening to the tour guide. We ate on the bus to maximize time at the different locations. Not a ton to eat at Stonehenge, so it's better to grab food at windsor in my opinion. The time at each location was brief but I felt like the tour guide was spot on with his recommendations for how to see things. Bath has lots of cute shops and we had delicious pasties, scones and chocolate. If you absolutely must read every plaque and sign, this tour is not for you, but I was very happy with getting to see all these places with a tour guide that kept things on time! I only had so many days on vacation this tour checked off a lot on my list!

or, depending on traffic, somewhat later

Windsor castle was closed when we were there because the queen had recently passed away. We did get to to see the outside of the castle and shopped some in the little town. Totally worth it!!

There is no stops Apart from the ones that are on the itinerary

I thin its about 11 hours.

Yes, you can still get the ticket at the baths. You should check it out while there. It's pretty cool!