You can see most train timetables for Europe here: http://www.bahn.de/i… … and find most low-cost flights here: http://www.skyscanne…

BCN>ROM flights in June, for example, showing some as cheap as $50 with airline Vueling; LTN>BCN in June for $48 with Easyjet. Use “LON” to search all London airports; “ROM” for both Rome airports. If you end up taking the Easyjet flight from Luton, check out www.easybus.co.uk for inexpensive bus transfers.

1. Where were you looking for train schedules? As Don suggests, bahn.de, the German national rail company website, is the best for schedules anywhere in Europe.
2. Overnight trains will always require a reservation. Premier “name trains” and express trains between major cities usually require reservations. You can often avoid reservations by taking slower (because they make more stops) regional and local trains. If you want to avoid reservations, try clicking on “further options” in the timetable search box on Don’s link. You can then click “all without ICE” to filter out most of the options that require reservations or “only local transportation” to see only trains that don’t require reservations.
3. Barcelona to Rome is nearly 1700 km — 21 hours and 4 or 5 connections by the fastest and most direct trains. That’s not the kind of train trip that’s going to show up in any abbreviated time table.
4. As for “rail pass stuff.” This is really two unrelated issues. First, how to get from place to place. Train is often, but not always (like this Barcelona to Italy example), the best answer for that. The second question is which, if any, railpass is best. That depends on your exact itinerary, exact dates, travel style, willingness to do extensive research and willingness to commit to exact dates and times in advance. For a five week trip, the “best” option will probably be a combination of travel modes and a combination of ways to pay for them. Best may be some sort of railpass, a couple of cheap flights, some point to point train tickets, a bus ride or two and maybe a ferry.