anything to do with electronics can be tricky to diagnose, you have to wrap you head around the idea of troubleshooting sometimes.
Start doing the basics, and work backwards untill you pin point the problem.
Since your amp is heating up, it can be a couple of things
-Too low an impedance on the amp from the subs/speakers connected
-Short on one of the wires causing a resistance close to 0 to appear on the amps output
-Internal issue with the amp (bad power transistors, resistors burnt or shorted
Your best bet is to start by taking all the loads off the amp and run the amp and see if it gets hot or not. If it stays on (green LED should be on) and stays on for a long time you know your amp is ok.
If your amp still gets hot and shuts down with no load on the amp at all its something internal, or external to the amp itself (shorted outputs, ground problem etc etc)
Now lets assume your amp functions fine with no load, your next thing to check is how the speakers/subs are wired. If your running 6 speakers on a 4 channel amp, most likely 2 pairs are being paralelled together and connected to the amps output. Your amp might not like running at that configuration, you have to check out the user manual for it. It would listed lowest impedance load at 4 ohm mono, 2 ohm stereo etc etc.
Your best bet is buy a multimeter if you really want to diagnose it on your own. It is one of the best investments for electronic troubleshooting.
If you have a multimeter check out what impedance you are reading on the speaker setups. You should have around 3.4-3.8 ohm for a typical 4 ohm speaker connected to the amp.
As for your batteries getting drained, how is your remote wire connected? Your remote wire comes off the deck and tells the amp to turn on/off whenever the deck is on/off. You shouldn't be draining your battery if the remote wire is connected properly. When the key is turned off in the boat, it kills the ignition and the ACC for the deck, which shuts the deck off, which also turns the amp off, so you dont forget and drain the battery.