A couple of thoughts about the topics. The weather in the Med (which covers a huge area) varies considerably from place to place. For example, Rome can be very hot and humid on a summer day wheras it might be delightful on one of the Greek Islands.
Regarding the post about getting "pushed" through the Vatican....that is a problem with many excursions (especially cruise ship excursions) where they have ambitious itineraries and must keep to a schedule. We have been through the Vatican multiple times and are never "pushed" because we simply go on our own. When you make a choice to take tours you get what you get! When you do it on your own (or book a private tour) you can set your own pace and agenda.
As to October/November weather (we will be in the Med this Oct and Nov) it really depends on where you are and a bit of luck. It can be comfortably warm in much of the Med during those months (we have been in Barcelona in early Dec when it was in the high 60s) or it can be chilly. One nice thing is that its outside the normal "season" so things are not as crowded. The downside is that you are probably not going to be swimming on the Riviera or even on Mykonos.