Is it common for gutters to drain into a septic tank?

It's not likely that all of those gray water systems are draining into your septic system. Here's why, with that much water going into your drain fields they would have had a problem by now. Even a single running faucet drip can overload your drain field. They're made to get wet, than dry, wet, then dry. If it's wet all the time, it will fail for a couple of reasons we won't talk about now. Another reason I don't think so is if the previous owner was talented enough to do all that work, chances are he was smart enough not to overload his system. If they are, get them out of there and set up a rain barrow system for watering yard plants and gardens. You may have two systems installed, one for black water and one for gray water.