1) Rain:
http://www.hydromet.gov.bz/climate-summary Generally dryer in the north, wetter in the south, cooler in the hills.
2) Beaches: There are some beaches in the Corozal *District* but none to speak of near Corozal Town. All beaches in Belize are public though some you might have to access from the water. Generally speaking, the cayes have the best beaches (but you can't beat Hopkins!)
3) Where to Stay: In Corozal? Budget but very clean and nice Sea Breeze Hotel (
www.theseabreezehotel.com). Upscale/resort The Almond Tree (
www.almondtreeresort.com). For everything else, check out TripAdvisor.com Edit: A little further from town (but they'll pick you up and have a beach) there is Cerros Beach (
www.cerrosbeachresort.com)
Good luck!