Correct, the compaction needs to be done with a heavy compactor. Typically those are rated to compact a 12" lift of the proper material at the correct moisture level. The material should be placed at a 12" maximum depth then leveled and if things are very dry and dusty it should be watered and let soak in, then at a very minimum 2 passes with the compactor ( I always go at least 3) . The other alternative is to use the clean stone like they did under the floor, that does not require compaction. This is more expensive however you do not need to worry about your contractor using correct compaction techniques (most do not).
If you were given details on the Size and spacing in your contract them be sure to check that. This is supposed to be checked by the local building inspector, However building inspectors come in all different shapes and sizes, some are knowledgeable and dedicated to there profession and some are not..
Do make sure there will be a minimum of 3" concrete around the rebar. It needs to be held off the forms and bottom that minimum amount.
Sorry for the confusion. They are the same. The gravity drain I described is also called a wick drain.
A catch basin is a structure used to "Catch" surface water and put it into a drainage pipe. So you would not be putting a catch basin in the gravity drain I described. A "sump" is a vertical structure (usually just a large diameter pipe ) that is used to gain access to the ground water table so you can monitor its level and install a pump when necessary to lower the ground water. These sumps can have drain lines that collect the ground water going into them and / or outfall drain lines that go to daylight to drain the ground water.
correct.. All is not lost. You can still dig down to the very edge of the pool bottom and expose the stone stone he placed under it. You should be fairly wide when you get close to the pool bottom and as close as he can get without undermining the pool and start your drain there with plenty of stone around the beginning of the first 10' of perferated pipe.
Post back with the elevations of bottom of pool and creek bed if you decide to install the drainage.