Hydration is something you have to work out individually during the training cycle to figure out what works best for you. What distances are you racing? Quick answers - yes you can wear a fuelbelt on the run if you would like. I sweat like crazy, and my body requires a good bit of fluid. Step one is to make sure you are hydrated before the race. Don't wait until race morning and then start to drink water, you can't catch up like that. Be sure you are getting good fluid intake right up to race day. Loading up on race morning can lead to lots of quick trips to the porta-john before the race starts, and stripping your body of electrolytes before you even hit the water. All that said. I will typically just carry one bottle for a Sprint. Some go with nothing, but my body won't go for that. For the run in a sprint I will just get water at the aid station if I need it. Usually it will wind up on my head (by choice :-) ) during hot races, rather than down my throat though. You could go the camelbak route, but you may find it costs you far more time in T1 and T2 than it saves you on the bike.
Over thinking? Personally, I'm a planner when it comes to triathlon. In my experience planning and thinking through relieves pressure and nerves, but that's how I'm wired. I've yet to enter a race and say to myself, " I feel WAY too prepared for this one ;-) " Good questions you have. Best advice is to pick a hydration/nutrition strategy and then train with it like you would race to see how it goes. Hope you have a great first race!