A sea plane was just going around it. It was very loud and got like 10 feet from the shore. It's just going in circles and won't take off and leave.
As has been pointed out in other answers and comments, if the aircraft is taking off or landing, there are no regulations requiring distance from persons or structures, at least that I know of.
What you may be witnessing is an attempt to takeoff in less than optimal conditions. For example, if there is no wind and the surface of the water has no wave action, it can be very difficult to break away from the water sufficiently to get the aircraft "up on the step", in other words to get it going fast enough that it can plane along the front part of the floats (or the hull). Once the floats are "planing" on the water, with the lesser drag than if they are fully in the water, the aircraft may then be able to accelerate to takeoff speed.
The usual procedure if you're having trouble taking off from a wave-less water surface (often called glassy water), is to run back and forth at a high power setting with as much speed as you can get to generate waves. Then, at some point hopefully, as you run back across waves you've previously generated you'll be able to break free of the water because there's less drag running across waves, even small ones (ripples even) than glassy water.
I had to employ that procedure a few times back when I was flying floats, and I remember one instance when it took at least a half hour before I managed to get airborne.
Are seaplanes allowed to fly in residential areas?
I can't speak to current practices and regulations as I retired in 1999. However, back in the 1970s and 1980s when I was flying floats, we often operated in residential areas. For example, go to Google Earth and bring up Eugene, Oregon. Look at the area on the Willamette River immediately adjacent to downtown Eugene. You'll notice two bridges. We often operated alongside residental areas upstream and downstream of the bridges. We also operated between the bridges. Depending on conditions that sometimes meant flying under one of them, not an uncommon practice for seaplanes, and perfectly legal, at least back then.
If you don't have Google Earth, you can use the Google Earth browser version or see it on Google Maps.