Mbresso, I've taken this tour twice, and it's a great tour. I don't remember ever being told there are no elevators; however many European hotels either don't have them, or if they do, the elevators may be very small. Think, one or two people small.
I honestly don't remember if the hotels had elevators (we seldom use them, and we're older than you are,) except the one you'll probably be staying at in Palermo. I think it had one, but it doesn't go all the way up to the terrace level, which is where breakfast is served. So you'll have to be able to handle at least one flight of stairs at that hotel.
The phrase "they not touch our luggage whatsoever" is strange. The bus driver will load your bags onto the bus, but you will carry them out to the curb. And when you stop for the night, the driver will unload the baggage compartment; at that point you pick up your bag and cheerfully carry it to the hotel, which in most cases is not more than a block or two away. There are exceptions, as someone posted upthread.
Hence the importance of packing light. You'll find plenty of tips on this forum to help you whittle your bags down to a manageable weight, size, and number.
Two singles sharing a room are given twin beds. Married (or otherwise) couples usually have two twin beds shoved together. It says somewhere in the tour materials that if two singles are sharing a room, even if the two beds are shoved together, they will always be made up separately - separate sheets and blankets.
Breakfast and bus time depend on your guide, and on the scheduled activities for the day. One the last tour I was on, the guide liked to get an early start, so bus time was almost always 8:00(!) with breakfast available about 7:00 or so. Sometimes earlier, never later (except on our free days, of course.) I think you can assume you'll load the bus about 8:30 or so most days.
There will be lots of walking and hill climbing, so you might meditate on the reasons you're concerned about the lack of elevators.
When you do get ready for the tour, pack your bags and go for a walk. Be sure to include hills and stairs. Don't just walk around the living room and say "Oh, I can handle this!" Hills, stairs, and some distance. Then go home and repack. Repeat as necessary.
It's a good tour, but you're wise to ask these questions ahead of time.