We’ve never been to Italy or France or Germany, or anywhere in the Alps, or Eastern Europe.
... spending the whole time in Italy, to darting across the continent to 10-15 cities.
Darting across the continent to even 10 cities in 28 days is probably doable, but IMO would be a horrible waste given how many of those days will be eaten up by travel (if on time), checking out, getting to transpo, to the next place & checking in.
Great idea to
start with the weather, look at lows as well as averages, and wind chill can be chilling! Do you enjoy cold weather? You could easily spend the entire trip in any of the countries you mentioned above, although I agree I would avoid the higher elevation Alps, except for example, Lake Como in April should be fine. And personally, I would work my way from the south to the north, as it warms up into April.
Good Friday is March 29, Easter is March 31 & 'Easter Monday' is a national holiday in most if not all of Europe. School kids are usually on holiday from the Thurs or Wed before Easter through the end of the following week (i've checked a few countries including Italy recently.) So be aware of Easter break in terms of hotel prices & crowds in larger cities, that would be a good week to be in smaller cities.
If you want to go to Rome, I would start there first, it will be the quietest from March 23 - March 27th, (remember Easter!)!
Suggest you start with the public library, browse the travel section, watch lots of RS videos & travel blogs on this website, and take it all with a grain of salt because it only shows the beauty, not the crowds, cancelled flights, etc.
You mentioned road trips, as a first visit at that time of year to any of those countries, I would skip renting a car. The train services are excellent. Hiking can be done at lower levels. You can decide first where you want to go & then look at local hikes.
It's very likely that the closer it gets to the summer Olympics, the more expensive Paris and environs will become.
I would actually suggest having a look at hotel prices on a variety of dates to the places you might like to visit, it will be illuminating!! (I was checking out a 3-star hotel in Amsterdam the week leading up to Good Friday, it was 125 Euros, following week it was 250 Euros!). And that's before the tulip festival....
Good luck and let us know as your travel planing progresses!