Ernest,
A few thoughts on your questions....
(1). Especially with your very short time frame, using a budget flight is the best option. You may be able to book a flight using Alitalia from Naples, but not sure about EasyJet or Aegean at that time of year. You'll most likely have to transit via Athens regardless of which airline you use. You'll have more flight choices if you depart from Rome / FCO. The flight schedules for November haven't been posted yet, so it's difficult to check on what your options might be.
" We heard that Crete is a wonderful place to start."
IMO, you don't have for Crete with such a short time frame. I'd suggest focusing on Athens with perhaps a side trip to Nafplio or Delphi. That's more than enough to keep you busy for a few days.
(2). Not sure what to expect as I haven't been there that late in the year. It will probably be "quiet" and you shouldn't have any trouble getting a hotel booking. If you're planning to hire a local guide, it would probably be a good idea to contact them well in advance, as they may be operating on "reduced hours" at that time of year. Also check the opening times for the sights in that area, as they may also be on reduced hours. As I recall, there's information in the guidebook on the opening & closing times for the various sights in Athens.
(3.) Forms of travel - that will depend on where you're going. For a trip to Nafplio, I believe that Bus is the cheapest method (about 3 hours in each direction). For a trip to Delphi, using a local day tour company might be the best option (I haven't checked) or Bus (again, about 3 hours).