First step, if you haven't already, find a local chapter of the US Power Squadron and take their Boat Safety course.
http://usps.org/You'll accomplish several things. One being a safer boater, which is good for you AND everyone else on the water. Second, you'll have a chance to meet other local boaters. This will be handy for learning local conditions and possibly boat help.
I make this suggestion to all boaters, but especially to new ones. But in your case it's probably even more important to make friends with someone that can actually take a look at your setup. Used boats (like anything else) have the potential for all sorts of aftermarket accessories and add-ons. Some may not be done to factory standards. Someone that knows what they're looking at can often readily establish what's what.
The battery switch should, in general, have NOTHING to do with the shore power based charger. But this assumes it's all set up that way from the factory according to ABYC standards. If it was added after the fact then, who knows? Boat fridges generally can run off both AC and DC power (that's 110v shore power or genset, or 12v from the batteries). But, again, this depends on the particular units involved and how they've been wired. It's very difficult to diagnose this from online just based on text. And it's even more difficult when someone's new to both (not to cast criticisms here though).
The radio always works off 12v. If you're connected to shore power then the battery charger should be doing enough of a job to keep them charged (and thus run the radio). Batteries do wear out and chargers do fail.
Having someone actually LOOK at it all works wonders. Hire a local captain to give you some training on the boat. Most can take you through all of the systems on a boat and show you how it all works. You may also want to consider hiring a local marine surveyor and paying them to give the boat a complete inspection survey. This will warn you ahead of time if there's any lurking issues that need attention.
Sorry if this seems like a hassle, but when you're new to something it can be an uphill climb to get enough experience to be confident in how it all works.