For example, does the blood of the freediver accumulates in his/her head while being upside down, as it would on land, or not, as it would in microgravity environment ?
A freediver could not be in perfect neutral buoyancy. The air in his lungs causes his chest to be more buoyant than his legs. So he would be turned chest up, legs down. Been there, done that. If you let air out until you sink, the mean density of your chest is still lower than the density of your legs. When you exhale completely some air remains in your lungs.
If there is some water left in your mouth or in your diver's mask, it will flow to the lowest point of the cavity just like it would do when you are not floating in water. Just like within a submarine mentioned by Organic Marble.
But blood does not accumulate in the head while being upside down in the water. Rising blood pressure is compensated by rising water pressure when going down from feet to head.
There is a similar effect of fluid redestribution within the human body for a freediver, an astronaut and a participant to a bedrest study. Under the effects of the earth's gravity, blood and other body fluids are pulled towards the lower body. In zero gravity, in bedrest or in the water, the blood is shifted from the lower to the upper body by the elasticity of the blood vessels of the legs. The kidneys are activated to remove the excess water from the upper body.
The hydrostatic gradient counteracts rising blood pressure from feet to head. It does compensate it exactly only if the density of the blood is the same as the salt water around the diver.
An astronaut practicing an EVA in the Neutral Buoyancy Laboratory (a large swimming-pool like facility) is still affected by gravity. They are pulled down relative to the suit - which is buoyed up by its internal air volume and attached flotation devices. If they are upside down, the blood would tend to accumulate in their head.
Buoyant forces do not remove the effect of gravity on the internals of a floating object. Crewmembers do not fly/float about within submarines and an object dropped in a submarine falls as normal.
An astronaut doing an EVA in space is not affected relative to the suit. There is no buoyancy force and the same inertial forces affect the astronaut and suit.
The viscosity of the surrounding medium has a lot of impact concerning your ability to move. If, for some reason, your body starts rotating, you'll come to a rest quickly in water, but it'll take a very long time on the ISS (unless you can get a hold of a wall) and you'll rotate forever in free space.
In water, you can move around easily by swimming; swimming movements on the ISS or in free space won't have any effect except possibly make you wobble a bit.
One big difference is that a diver in neutral buoyancy still has his sense of equilibrium working correctly, as gravity still acts on the inner ear.
The main difference is that an astronaut in the ISS is in constant freefall at orbital speed, whereas the diver in equilibrium is not falling at all. That's why fluids in the diver will behave just as in a human standing around on land, if we only consider the gravitational effects.
The astronaut would have more similarity to a parachutist in that regard.