The tank that comes with R/O systems is a bladder tank. Those tanks have an air bladder inside which gets compressed by the water pressure. It will stop filling when the pressure inside the tank gets to high for the R/O system to overcome. Because of the air bladder you will not be able to fill all of the 2 gallons of your tank.
One option is to buy a bigger tank, but they are expensive.
The float switch should work and so should modifying a keg. You may be able to make a keg work like a bladder tank by not venting it when filling it with water. But that allows you to collect only 2-3 gallons. Seems that a large vessel and a float switch is a more attractive option.
The black manifold is a pressure booster that uses some of the effluent pressure to boost the pressure of the raw (i.e. incoming water). The system I'm using has one too.
The recovery rate, which is the amount of R/O water that is "recovered" from the input water also depends on the temporary hardness and pH of your water. If the pH is high and your have a lot of calcium and bicarbonate there will be calcium carbonate precipitation near the membrane due to the increased calcium and bicarbonate concentration. As a result it is beneficial to run a R/O system after a water softener. This only makes sense if you already have a water softener.
If your problem is high temporary hardness, as opposed to high alkalinity paired with sodium, you may also be able to use slaked lime to treat your water
. There is no or only little water waste associated with that technique.
R/O systems can be cascaded to get a better recovery rate. I think many commercial systems do that. But the cost keeps increasing while the actual return on investment decreases.