Not significantly. From Wikipedia:

Liquid water can be assumed to be incompressible for most purposes: its compressibility ranges from 4.4 to 5.1×10−10 Pa−1 in ordinary conditions. Even in oceans at 4 km depth, where the pressure is 400 atm, water suffers only a 1.8% decrease in volume.

To answer very literally, no. The water itself isn’t thicker, it’s the same. It is denser because the pressure is significantly higher, because the water is colder, and to a small degree because salt settles down

However I also wanted to consider what’s in the water so I did a bit of research and while there’s a higher density of salt at the bottom of the ocean there’s more bacteria and other small organisms higher up toward the top of the water. So if you’re only thinking about pure water than it’s the same but if you’re trying to compare water content it seems to be thicker / more condensed higher up

Water basically does not compress so no.

It does vary sightly, but it’s due to the temperature difference as you go down, rather than the pressure.

https://rwu.pressbooks.pub/webboceanography/chapter/6-3-density/#:~:text=Density is lowest at the,to the increase in density.

It is, but I’m not smart enough to explain why.