In other words, does it take more effort for fish to swim in very deep water than in shallow water.
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> Is water near the surface of the ocean less dense than deep water
Density is a measure of how tightly packed the molecules are in something. You can make most solid objects denser by squeezing or crushing them, thus reducing the distance between the molecules that make them up so they become “tighter”.
Water is an (almost) incompressible liquid, meaning you can’t change its volume (size) by squeezing or crushing it. After all, if you squeeze water in your hand it won’t do anything to it. What this means is that the density stays constant since the distance between the molecules remains unchanged.
So to answer the first part of your question, technically yes, but the surface is less dense by such a small amount that it can be considered a negligible difference. So for simplicity’s sake, no, it isn’t.
> In other words, does it take more effort for fish to swim in very deep water than in shallow water.
This is a different question not related to density, but rather weight and pressure. The deeper a body of water is, the more pressure there is at the bottom because the more water there is on top *pushing down* on you. At extreme depths like at the bottom of Challenger Deep, this pressure becomes strong enough to crush reinforced steel into a flat, soup like material.
So yes, it becomes exponentially harder for fish to swim the deeper they go, because they need to exert more energy to push against the enormous forces of water all around them. For this reason, animals that live in extreme depths don’t really have solid bodies, they instead have translucent bodies similar to that of a jellyfish’s membrane which won’t be crushed by the pressure and instead allows them to swim without much resistance. See images of the angler fish and some species of worms, mollusks and microorganisms that live in Challenger Deep for more info.
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