would a fish have more oxygen in a tank almost completely filled with water or only a third of the tank filled

Answer 1

The surface area of the water is what matters the most. If you're concerned about fish suffocating, fill the tank to the widest part and make sure there is good ventilation at the surface.

Of course fish do not breath the air directly above the water. The point is that the fish will need more than one tank worth of oxygen in its (their) lifetime, and the extra O2 has to come from somewhere - specifically, the air above the tank. The CO2 and O2 will exchange faster in proportion to the surface area. The more surface area, the faster the exchange. It doesn't matter how much total O2 is in the water as long as it is replenished quickly enough while the fish are breathing it.

Most fish tanks do not need a bubble machine to have enough oxygen for their fish; if you do need a bubble machine to prevent suffocation, you are probably packing the fish in too tightly anyway. You do need something to provide circulation, but a normal filter will do that anyway.

If for some reason your fish tank is going to be sealed for a while, such as transporting it, it is actually much better to leave a gap of air. Water holds about 10 mg/L of O2, and air has about 300 mg/L - you can see there will be much more O2 available for the fish if you leave them some air to go with the water.

Answer 2

Completely filled. Fish get their oxygen from the water, therefore more water = more oxygen. The air that is separate from the water is irrelevant, since a fish can't use this as an oxygen source, anyway. Air from above the water doesn't readily mix with the water below on its own - it usually needs to be bubbled through the water so that it can mix with it.

Answer 3

If you were concerned with the tank's pump and purification process breaking down, you would want the full tank. If not, it probably would be happy with one-third the tank full, unless it was a biggie and needed some more wiggle room.