14/2 Milan-Venice: book via tickets.oebb.at and save €4. Do NOT use "Seat reservation only” but add the Interrail/Eurail discount and then look for normal tickets.
17/2 Venice-Rome: book via tickets.oebb.at and save €4.
20/2 Rome-Genova: I'm not sure why you're travelling via Naples. There's a direct train Roma Termini 18:27 - Genova P.P. 23:20 (book via tickets.oebb.at for €10 per seat). The night train leaves Roma Ostiense at 0:14. You can save €3 by booking the night train via Italiarail.
22/2 Genova-Ventimiglia: Use a reservation-free regional train. Or book via tickets.oebb.at and save €4.
23/2 Marseille-Nîmes: there are direct reservation-free regional trains at 8:23 and 23:22, taking 1h 15 min, and save €44.
24/2 Carcassonne-Narbonne: just take the reservation-free TER at 18:20, arrival in Narbonne 18:51, and save €44.
24/2 Narbonne-Barcelona: book by phone via SNCF and save €4 (press #85 for English; reservations are sent via email). Or travel via Portbou using regional trains, eliminating the need for reservations entirely.
None of the booking methods above require a place of issue for the passport. ÖBB don't need many details at all.