Sorry for my reply in advance as I can't see the video at the moment.
Is that a right-hand drive/British vehicle? If that's the case, it's coming from either the oil pan or the crankcase pulley area.
If it's a left-hand drive (which I suspect), then the oil is probably coming from the tranny like another poster indicated. Is it black in colour or more amber/clean? Black is almost surely engine oil so check the oil filter and heat exchanger area for leaks (right down in front under the intake piping).
Amber coloured is almost surely tranny oil, probably overheated the bellhousing and gearbox and now you've cracked the seal. You can see the bell housing by standing in front of the car and looking to the right hand side also under the intake piping.
To check in behind the bell housing, if you lean over the engine check between the cabin bulkhead and motor, you should be able to see the exhaust piping coming from the engine, to the right of that you can probably see if there is any pooling on the underbody panel. It could be running alongthe panel off to the side so it's important you locate the source of the leak.
You should also check your engine oil level to see if you've got any significant loss.
Re: the clutch smell -- mine was slipping badly and when they replaced it I asked to see all the parts (it was done as a warranty claim). It stunk up the entire service bay at the dealer, horrible, horrible lingering cloying smell. Not surprised it took some time to disperse.