Hi, yes almost all trains are included. But mostly high speed trains needs a reservation. This can cost between 10-38 Euro. Depends from train to train.
Basic you can check railplanner app. But it is not up-to-date and some data is missing.
You can use bahn.com for basic search.
For me best is to travel via Germany to Brussel. In Germany, Austria and Switzerland high speed trains have only optional reservations.
You can also use nighttrains like Rome-Munich or Innsbruck/Munich/Zürich-Amsterdam and change in Cologne to the ICE to Brussel.
Also a possibility is to travel via Ventimiglia and Nizza or with the TGV Milan-Paris and Thalys Paris-Brussel.
Frecciarossa Milan-Paris is not included. All other trains of Trenitalia yes