May isn't high season, so Jadrolinija could post May schedules any time after the first of the year (late January would be my guess). Their customer service center is very helpful and has people fluent in english. I'd suggest contacting them via e-mail (there's a link on the Jadrolinija website) and asking when May schedules are expected to be posted.
My recollection is that Jadrolinija didn't do daily crossings last year, even in high season. In May, there will likely be 3 crossings per week.
Best option from Dubrovnik to Split is bus. There are several per day. Ask your hotel or sobe to call the bus station and reserve tickets. You can then pick them up and pay for them when you arrive at the bus station. Be sure to have them ask how long before the departure time you must pick up your tickets.
I don't believe Jadrolinija ran the Dubrovnik to Split ferry service in 2013. To go by boat, you may need to first get to Korcula town and then take a Krilo hyrdofoil from Korcula town to Split.
From Split to Zagreb, train or bus are your best options. I'd investigate both options and pick the best one for your itinerary. Zagreb is great, so budget at least 1 day to see its sights. There are some very good pizzerias (yes, Croatia has great pizza) on a street behind Jelacic Square (think its called Skalinska).
