Ok... how do I say this carefully?

When you're in Eastern Europe (this isn't nearly as bad as in western Europe), just be carefully around gypsies. Most of the ones you see on the streets are probably harmless and just begging (or selling kids toys), but they are known to potentially get violent as well.

Also, I think you are not giving yourself enough time to actually explore these places. Now I haven't been to Europe since college, but I found that I needed around a week to explore one city to my liking. I understand if you want to go to as many places as possible, but you will likely be rushing and missing quite a few landmarks on the way.

Edit: Guy below made a good point - Europeans don't really like Americans personally (except for the British). So if you want (this is what I always do), simply get a Canadian pin or flag or whatever and put it somewhere were people can see. Everyone loves our country, so you should be treated much better if you do this.

As an Belgium I got hurt reading this but then I saw you link 'Vlaams' as Flemish(Belgian) fries and can only agree =p.

Anywan one tip, in some regions just say you are Canadian people will treat you better and make even silly 'eh' joke sentences. (Also you miss out on not going to Bruges).

In Italy traffic is terrible and trains never arrive in time so good luck getting in and out of the country in one day. Rome has too much to see in one day, you might consider visiting it at a later date and replace it with some Northern Italy locations like Turin, Milan or Venice so that you shorten your trip and get more time to spend visiting more places, you'd also be closer to Switzerland for the next day

Come have a beer with me in Amsterdam, I work there. It's a small city.

My advice would have been "Make that trip in the summer", but that's probably no option anymore ;)

I was very satisfied with the Italian train service when I used it last year.

went from Milan to Turin, Rome to Florence, Florence to Pisa, Pisa to Florence, Florence to Venice, Venice to Bologna, Bologna to Rimini, Rimini to Bologna

all trains were pretty much on time.

It depends on what you're doing, but personally I think 2-3 days for big cities is enough.
Most of the time "wasters" are museums, zoos or shops.
Why visit a museum of natural history in different cities? They mostly have the same exhibits.
Same for most zoos or shops, as they are the same around the world. I do however recommend shopping and drinking in Prague. It's extremely cheap there.

I know this isn't a suggestion of a specific place to go to but try to learn a couple of basic words and phrases in the native languages of the places you visit. When I went to Mexico, I found that speaking Spanish with the locals made their lives slightly easier and showed that some tourists actually wanted to respect the lifestyle and culture of their country. They seemed incredibly happy and grateful that I was even making an attempt to do so. Do this, and you are much more likely to receive help from the locals on certain places to go to.

did you travel with Freccia Rossa or Italo ? Those are the main high speed lines but they are more expensive which isn't the best for a group of friends

Right! I can't speak for other countries (except France :p) but here most people don't speak English, if you need informations try asking to someone young so it's more likely for them to know English, otherwise here's a few of the most usefull (and different) translations:

Toilet - Bagno

Station - Stazione

Water - Acqua

Lost - Perso

Use the mass transit systems in Europe, it's the easiest way to get around. I'd probably honestly pass on doing too many things like museums/zoos/etc. These become largely "samey" after a while, but if you can visit palaces and historical monuments I'd go for that.

Check out the Sex Museum in Amsterdam, that's good for some fun. Hell, check out one of the ladies in Amsterdam too, lol. Boat tour on the Sienne river in Paris is something I'd reccomend, really enjoyed that. Even though it's touristy, Eiffel Tower is worth seeing, I'd reccomend going a little bit before sunset, so you can see it in the day and then also at night when the lights come on. In London check out the Tower of London and London Bridge, there's a ton to see there.

You like are going to hit a wall of exhaustion at some point your trip, that's ok.

Take lots of photos, not so much of the tourist attractions themselves, but of you and your buddies. You will appreciate those photos later on.