Sicily trains need booking advance?(Catania to Siracusa)

Not necessary to book in advance. In fact, a bus may be more convenient. Bus stations are very near train stations in both cities.

Just allow time to buy the ticket. I have run into lines in Italian train stations that were long and/or slow enough that missing the train was possible--and on one occasion I did. You may end up behind someone buy multiple tickets to a hard-to-reach destination or a purchaser who's a good friend of the ticket-seller (which is why I missed my train).

To add to acraven's remarks, you can get stuck behind someone in need of a travel agent more than a ticket seller.

You can avoid lines at the station ticket window by using the automatic kiosks. The kiosks have instructions in the language you select and English is one.
The kiosks may require chip and pin credit cards, but if you don't have one you can probably use your chip debit card, which certainly has a pin, or also euro bills (kiosks accept cash and give change back) since the cost of your ticket is low for that short distance.