Need help Italy Itinerary for honeymoon

Congratulations! Although the desire to see as much as possible is certainly understandable, you really can't fit all of this into your time frame and really appreciate any of it. I would suggest three or max four locations only. How about 2 nights Lake Como, 4 Venice, 5 Florence, with a day trip or two, and the remainder in Rome?

I would cut something out; You have too many places and not enough time but you might do something like this:
Leave April 12
Fly into Venice
Venice April 13, 14, 15
Train to Varenna
Lake Como April 16, 17, 18
Train to Milan
Milan April 19
Train to Monterosso (Cinque Terre)
Cinque Terre April 20, 21
Train to Florence
Tuscan Agritourismo April 22,23, 24, 25
Train to Rome
Rome April 26, 27, 28
Trains to Sorrento
Sorrento April 29, 30,
Travel to Naples Airport
Fly out of Naples May 1

I like Jazz itinerary although I would select either the Cinque Terre or the Amalfi Coast. If you skip one, you’ll save some significant travel/transfer time and can stay 3 nights at one or the other and add a night to Rome in Jazz’ plan.

The only place you would need a car is if you stay in the Tuscan countryside. If you stay in Florence, no car. I would absolutely not have a car in the CT, Amalfi Coast, nor at Lake Como. The trains will serve you well everywhere, with the occasional bus for a day trip or in a city.

Do you have Rick Steves’ Italy guidebook? It will be invaluable in planning and understanding transportation.

Congratulations on your upcoming wedding. Full Disclosure: I'm an old-fashioned romantic. To me, a honeymoon is a little different than any other trip to Italy. It's a celebration of a new life together in the world's most romantic place. I personally would want to do more lingering and less racing, more slow walking hand-in-hand and less running to catch the next train, more staring into each other's eyes over a glass of wine under a Tuscan moon and less checking in/out of hotels. So, I personally would pare the list to 4-5 bases -- 6 at most. BUT that's totally personal opinion. I would consider picking one coastal destination and adding more time there instead of trying to hit CT and Amalfi Coast. You could do something like Amalfi Coast --> Rome --> Florence/Siena --> Venice --> Como --> Milan (day before flight out). Think about "open jaw" flights: fly into one location (e.g., Naples or Rome) and out of another location (e.g., Milan). That gives you 3 nights at each stop + 1 night in Milan + 2 nights to add to your bases.

Once again, Congratulations!

I agree with Dave: to me, a honeymoon should be a time to relax after the excitement & stress of the wedding and all the preparations that have gone into it. It should be as stress-free as possible.

You asked, "Is it possible to cover this much ground in the days we have?" The answer is, yes, it is humanly possible, but in my opinion not at all desirable -- even if you weren't on your honeymoon! Only two days for Venice and one day for Florence? That short time would be frustrating to me.

You'll find plenty of "history, culture and experience" anywhere you go in Italy, so you don't have to feel that you're missing out when you eliminate some of the destinations on your list. You have 18 nights on the ground in Italy. I would say to choose no more than 4 or 5 destinations and stay 3 to 5 nights in each.

Is it possible to cover this much ground in the days we have?

You can 'cover' that much ground but it will be a miserable experience, in my estimation

Lake Como, Cinque Terra and Amalfi coast are three "waterfront" destinations. With the time you have I would suggest you pick one 'waterfront' and give yourself enough time to stay long enough at your destinations to enjoy them.