The order of the oil pressure system is right. From pump (internal to motor) -> external oil filter -> oil cooler -> adapter plate.
The oil breather tank (the one with the filter on) is where fresh air is drawn in through. Normally fresh air is drawn in via a tapping in the intake tract just after the air cleaner. The breather tank replaces this. Hence the line from the rocker cover (previously to the intake tract) now comes from the little breather tank with the filter.
The oil/air separator tank (catch can) is connected in series with the original PCV (positive crankcase ventilation) system before the point where the PCV valve connects to the intake manifold. The idea is that the catch can separates any oil vapour from the air being sucked into the engine. (The oil vapour normally reduces the octane rating of the air/fuel mix.)
The inlet to the oil/air separater from the crankcase goes into the lower pipe on the tank and the cleaned air is drawn out of the top pipe of the tank into the inlet manifold. The oil/air separater should also have a little drain tap at the bottom that needs to be periodically drained to release any built up oil.