What would WhatsApp offer that something like Facebook Messenger wouldn't?
Facebook actually now owns WhatsApp, but they remain separate apps. They compete not only with each other, but with things like Signal. Features that appear on one often start appearing on the others, so you can usually do similar things with all of them. But with all such apps, all parties have to have the app on their phone.
So, if you and the people you want to communicate with are already on Facebook Messenger, see if it does what you need. I haven't used it and so can't comment on how it compares with WhatsApp.
The specific advantage of WhatsApp is that a huge percentage of the world outside North America uses it routinely. They are often shocked that many in the US have never heard of it - it's so ubiquitous in other places. I saw a YouTube video by German woman now living in the US, who explained that very few Germans use regular SMS anymore - everyone sends these kinds of messages on WhatsApp. If you want to communicate with anyone abroad (say, the owner of an apartment you're staying in, or a tour company representative), they're likelier than not to have WhatsApp.
In other words, even if you're using Facebook Messenger to communicate with friends and family back home, you may want or need WhatsApp as well.
A fun feature of WhatsApp (and, I presume, other similar apps as well) is that when you get it, you can see everyone else in your phone contact list who has it. You may be surprised at how many do - I sure was!
Is the MMS/SMS issue unique to Italian data plans or EU wide?
As some of the examples above indicate, what a plan charges for which services is not about the country, or group of countries like the EU. It's about the particular rules of the carrier and the specific plan you have with them. For instance, long ago in the flip phone days, I had a pay as you go plan from T-Mobile. Calls were $0.10 per minute (higher if you bought a smaller allotment of minutes), SMS was $0.10 each, and MMS was $0.25 each. Other T-Mobile plans had different prices for each of these.
Before buying any plan, it's important to figure out how you're going to use it, and make sure you understand the prices for each of the services you'll be using, what services you can't use, and what non-included services cost if you do change your mind and use them. For instance, let's say you don't expect to be making calls to the US, so you don't get a plan that advertises a good rate for this. What if there's an emergency and you end up making calls to the US after all? Will they be €0.09 per minute, or €2 per minute?
