Do buses run on Easter Monday from Catania to Siracusa?
Sunday buses in Sicily are dicey. Holiday buses in Sicily are dicey. Honestly, I wouldn't count on anything based on information posted on the internet. I'd want to get the information on the ground, at the train station.
However, I've just checked the Deutsche Bahn website, and there's a train leaving Catania at 10:38 AM, arriving in Siracusa at 11:53 AM. There are also departures at 4:32 PM and 5:22 PM, plus three later trains, so it looks like you have an ironclad solution. The 5:22 PM and 9:29 PM trains are InterCities, which I think require seat reservations (and could sell out), and you might save a few euros by buying the ticket early. The other four are regional trains, so there's nothing to be gained by trying to buy their tickets early, except that you don't want to be stuck in a long line at Catania Centrale when your train is about to leave.
To confirm the schedule and the fare from an Italian source, use the Trenitalia website.