Brussels: Brussels Airport has a train station right underneath the airport. If you're visiting Brussels first, then there are frequent trains to the city centre; tickets can be bought online or at the station from ticket machines or the ticket office. Price remains the same for this. Brussels has a lot of train stations, so it's a good idea to check which one would be closest.

Brussels - Amsterdam is served by Thalys high-speed trains and hourly Intercity trains. Tickets can be booked via NS. Thalys is faster, usually more expensive, only serves one station in Brussels and your ticket is only valid for a specific train (changing is sometimes possible, at a cost). The earlier you book, the higher the chance for cheaper tickets.

The intercity trains Brussels - Amsterdam serve 3 stations in Brussels and Brussels Airport, so you can also take this train directly from the airport. Booking (best via NS) at least 7 days in advance is cheaper; your ticket is not linked to a specific intercity train but can be used on any train on this route (except Thalys/Eurostar) on a specific day. Children under 12 travel for free if indicated at the time of the booking. There are no seat reservations on these trains.

Amsterdam - Berlin is served by direct IC trains. Schedules and tickets best via Deutsche Bahn; seat reservations can be added. Again, children travel free, this time if they're under 15 years, also if indicated at the time of booking. The earlier you book, the less tickets cost.

Berlin - Prague is served by direct EC trains. Schedules and tickets either via Deutsche Bahn or Czech railways. Do compare these two because one may be cheaper than the other. Again, the earlier you book, the less tickets cost. With Deutsche Bahn, children under 15 travel for free; with Czech railways, children under 6 travel for free and under 15 pay a small price. In both cases, an optional seat reservation can be added.

I'm not sure if a Eurail pass will be cheaper. That will depend on the normal fares that are available and the amount of flexibility you need. Cheap normal tickets can often not be changed. With Eurail, the Brussels Airport supplement will be extra (it's already included with normal tickets from/to Brussels Airport). Seat reservations will also be extra: Thalys (mandatory), IC Amsterdam-Berlin (optional) and EC Berlin-Prague (optional).

Thank you so much for your help! really appreciated it!