Public transportation available for this itinerary?

Yep, everything reachable by train, except Castelrotto, which is a bus from Bolzano train station.
8 destination in 14 days seems to indicate you like riding trains.

In the interest of reducing hotel changes, I suggest that you visit Verona from Venice. Two nights is not enough time for the two lakes. Pick one. Stay three nights in Florence. Siena can be visited as a day trip from there.

Or hit Verona for a half day on the way to Castelrotto.

Yes it can be done, as others have said.

You don't have enough time for all the destinations you want - they will become a blur.

As some others have said, you don't have enough time to do these many places justice. I'd skip Florence altogether, if all you can give it is one night, or spend 3 nights there and do Siena as a day trip. 2 nights isn't enough for two lakes (Como and Maggiore). If staying in Varenna for 2 nights, you only have time for Como. Add a day to Venice and do Verona as a day trip

Have you already purchased your plane tickets? If not, the Venice Regatta is Sunday, Sept. 1. You could fly into Venice and fly back home from Milan. It’s a great photo opportunity and fun to attend. We just sat along the Grand Canal - didn’t buy a seat in the stage area.

Also, Verona will be in their last week of the operas at the Roman Arena. You wouldn’t want to miss watching one under the stars in this historic arena! Buy your tickets on-line. I sat in the section last September that’s still chairs, but not on the floor section. Great seats for a decent price.
https://www.arena.it/arena/en/pages/schedule-arena-di-verona.html

Agree with others; either see Lake Como or Lake Maggiore - no time for both. If you decide on Lake Maggiore, stay at Stresa. You might be able to catch an evening activity with their Stresa Music Festival when tickets go on sale. (Sign up to be notified, if interested.)
https://www.carnifest.com/stresa-festival-settimane-musicali-di-stresa-2019/

Now to answer your transportation question. Go to www.rome2rio.com and you can enter any two locations to see what transportation options are available. (It’s also helpful to see how to go from hotel and museum, etc.)

Personally, you are trying to cover too many sites with distance between them. Look up each transportation option and then write down how many hours it will take to arrive at the next location. If you have two days at a location, but it take half a day to get there, check into a hotel, etc. and then walk around and get oriented to the town, you really only have a day and late afternoon/evening. It’s always a good idea to have a third day there to have time to enjoy the ambiance!

As much as I love the Dolomites and Cinque Terre, I would consider dropping one of them since they’re the outliers for distance & transportation time. Then allow those extra days to ease your travel pace, especially since it’s your first time in this beautiful country.

rome2rio is a secondary source and not always very accurate.

https://www.trenitalia.com/tcom-en is the site of the Italian National Railway. They operate the trains and set the prices. For Castelrotto, use https://www.sii.bz.it/en/mobility-info for schedules and prices of buses in that area.
Be sure to use Italian city names, Firenze for Florence, Venezia for Venice, Milano for Milan.

One issue is that there is a nationwide schedule change on June 8-9, so you will not find the actual schedules until that date, but you can use it now for dates before June knowing that there will probably not be any major changes.

You need one more week or 2-3 fewer destinations.

You can go to all those places but in that space of time, your enjoyment factor will likely be minimal when it's all over

My $0.02

I vote with Joe. To me, there are far too many places on this itinerary with durations of stay at least one night below what I'd consider the minimum. I note, though, that you're experienced travelers, so if you've hopped around like this before, I guess you can be reasonably certain it will work for you.