Okay, there are several things I'd like to address. First, in my hypothetical model, which I may have oversimplified, the 1ft of water per acre was supposed to be inclusive of the runoff. I didn't know whether I wanted to explain it with or without the runoff in the model presented and I indeed confused myself since I did say that it'd be rare to rain 12" in a short period of time. I was going to have it rain 1" in my hypothetical situation over an area of 12 acres, which would provide the equivalent volume, however the composition of the runoff water would be different than it would be had it rained directly over my hypothetical lake because the runoff would have accumulated nitrogen containing compounds, salts, wastes, etc. and I thought it would be too difficult for most people to understand and for myself to keep track of. Boy was I right lol.
Next, what you should also consider is that water seeks the lowest point. I'm sure you understand this but think of the consequences involved. If a lake is the drainage point of all of the runoff in a large given area it is going to be a deep lake with a small surface area, a shallow lake with a large surface area, or somewhere in between the two extremes. The respective volumes will be the same, and the shape of the lake will be determined by the geography of the surrounding area. This means that my hypothetical lake may be 100 times the volume I gave it for example, if it is the source of drainage for many acres of land. What I'm trying to say is that the volume of the lake will be proportional to the volume of the runoff rainwater and groundwater (drainage to the lake). You could say that the lake deals with hundreds of square miles of drainage of surface water, but if you do so you would have to understand that the lake would be larger in volume to start with. Do you understand what I'm trying to say here? My point is that the changes aren't immediate and drastic like you are trying to say they are because if a large volume of water is heading downstream to a lake, that lake is going to be large anyway so it won't have a large impact on the lake.
You are correct that near the mouth of the river and where it empties into a lake/sea/ocean the water will be different. I think freshwater stretches 1 mile or more out into the ocean where the mouth of the Amazon pours in. However, there isn't an solid "border" so to speak where one side is FW and the other is SW. It gradually increases in salinity from the mouth of the Amazon to the middle of the ocean further away from the mouth of the river.