Rail or Flight

Phew...that's an ambitious schedule! You'll spend more time traveling than actually seeing the sights. If you can, you might want to leave a stop or two out so there's time to enjoy the cities!
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The choice between rail & air depends on where you are traveling, dates and prices. The cheapest plane tickets are usually on discount airlines & get increasingly expensive the closer you get to the date. The cheapest prices are often onsale 2+ months in advance - probably not available for your trip - and not always at convenient times. Sometimes the same with rail tickets.
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Remember with air travel, you have to count travel time & cost to the airport (not always close by), as well as the time to check-in and get through security (2 hours minimum). Train stations are usually in the center of town, so even if the train travel time is 2+ hour longer, it may be much faster overall, plus no limits on size and weight of luggage.
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Others can probably help on advice between the specific cities.

Slow down. You have way too much travel in there. You are attempting to travel to 4 countries with 1 or 2 nights in each. You will NOT see anything and will stressed from the attempt.

I'd recommend skipping the Cinque Terre and Rome this go round. You might also think about NOT doing Amersterdam. If you are flying into and out of Germany, why not spend some time there? Munich is wonderful, and there is lots to see in Southern Germany.

Spend at least 3-4 nights in any one local and you will enjoy your trip a lot more, plus this will take some of the stress off your planning how to get place to place!

Yes you are trying to do way too much there. You are not going to have enough time to really experience things.

Rail vs fly depends on where you are going ect....Train I think is ussually always easier but not necessarily cheaper. Same with the rail pass, it is not always the best deal. You need to figure it out.

our next trip we are going a mix of rail and flight.

OK, we agree, we need to, and will, pare back the agenda. I'll post again within the next day or two and let yall see what it looks like. As well as my thoughts about travel between the sites that we slim down to.
Thanks,
Mike

ok, is this a better plan ?
2 nights in Heidelberg
3 nights in Paris
2 nights in lake como
2 nights in cinque terre
3 nights in Rome

On your revised itinerary:

How are you going to connect these far-flung dots?

It doesn't look like there is enough time.

Am I missing something?

You are trying to go on what are really three separate vacations, combined with waiting until very close to your departure to plan for any of them! That might be feasible, and fun for you and your travel partner(s), if that is how you prefer to operate. In your favor is that you are going earlier than the bulk of the crowds, so that you shouldn't have problems finding hotels (or whatever kinds of lodging you prefer)at the last minute. Maybe your best bet is just to get a RailPass, giving you the opportunity to go wherever you want and you will fiugre out the train system when you get there- I would definitely not suggest flying around, since you have so little time and, as already posted, wouldlose so much of it just getting to and from the airports served by EasyJet or RyanAir.

When you factor in the costs both in time and cash of travel from airports to and from cities, the cost for flying is higher than it seems. There are differing luggage restrictions on airlines, none on rail.

Tix for trains are easily bought , from machines if you like. English language is the British flag. If you are distressed at the scheduling, buy the tix at a travel agent. We have trained all over Europe and have had few problems.

Only when time is at a premium do you need to fly

Costs for flying might be more expensive figuring the flight and ground transportation, but is definitely worth the expense if it saves time. I'm not familiar with transportation between Heidelberg and Paris, so I can't comment on that. For Paris to Italy, I suggest getting a flight on Easyjet or Vueling from Paris to Milan. Once in Italy, just take the train to your first destination. You can book all your train tickets for within Italy once you get there. No need to book more than a few days in advance.