Cheese is very slightly less dense than water. We'll pretend that it is exactly the same density. Then with a little bit of math we can calculate how much cheese will fit in a mold.
The volume of a cylinder is pi x r x r x h, where r is the radius of the cylinder, h is the height of the cylinder, and pi is 3.14159.... We're going to do this in metric because it makes it *much* easier. You can convert to imperial at either end, but to calculate in imperial requires a brain much larger than mine. Because we're pretending that cheese has the same density as water, then 1 ml of volume weighs 1 gram. 1 ml is also 1 cubic centimeter. This is why metric is always the way to go...
Let's take your 6.25" basket. First convert to cm. The internet tells me it's 15.875 cm. That's the diameter, of course, so we divide by 2 to get the radius. However, that's *awfully* close to 16 cm, so let's make the radius 8. We want to square that and multiply by pi. The square of 8 is 64, times 3.14159... = ~ 204. This the the area of the circle. Because we increased r a little bit, let's just call it 200 square centimeters. For each cm of height, it will thus weigh 200 grams (because metric is great). So if you have 500 grams of cheese, it will take 2.5 cm, or a little over an inch. If you basket is 3.75 inches deep, that's about 9.5 cm, which is 1900 grams, or apparently about 4 lbs 3 oz.
Of course, you can't make a 1900 gram cheese in that mold, because you need space for draining. It depends on the type of cheese, but basically you will end up with about half of that, so about 1 kg (or just over 2 lbs).
The amount of milk you use depends on the yield. Most cheese, before aging, will have a yield of 10-15% So if you start with 6 liters of milk, you will end up with between 600 and 900 grams of cheese. The 600 gram cheese will be 3 cm thick (1.2 inches) and the 900 gram cheese will be 4.5 cm thick (1 3/4")
Typically you would use 8 liters of milk for a mould of that size and for some cheeses you could go as high as 10 liters.
I hope that helps! (And I hope that I didn't make any mistakes. Best to do the math yourself!)