In prototype cars a few did have transaxle oil weeping out the vent.
Think about it this way. This gearbox has an internal oil pump that lubricates and cools the gears and bearings under pressure. Assisting in making this box one of the most efficient gearboxes ever built.
So you have more oil spraying around inside. Than a typ. gearbox without a pressure feed system. And some of this oil vapor is making its way out the vent.
On a few of the Protype Ford GTs. That was used for track development.
I relocated the vent to a higher position.
As for a trans cooler- that loop on the top of the gearbox is under constant pressure when the engine is running. And is the place to tie in a trans cooler.
DO NOT install a thermostat. As you may disrupt oil flow. But a cooler is a great idea. And the ford Racing unit is a very nice unit (if I do say so myself) it is a straightforward install. That fits nice, and will perform flawlessly.