Can I buy a ticket from Budapest to Zurich and have two interruptions or do I need to buy individual tickets for each "leg"?
Yes, you can buy one through ticket. But it might be not the best idea, since the ticket allowing stopovers will be rather expensive (should be 124 euro, because it will be issued using full international fare. While if you do buy three separate tickets, you have a chance to use discounted ones, thus pay only 13 euro for Budapest-Vienna leg, 19 euro for Vienna-Salzburg and 29 euro for Salzburg-Zurich, making it 61 euro for the same itinerary