Car appreciation... the aesthetics, the engineering, etc

Mrs Savage has got a Peugeot 107 five door. The rear passenger door seals can fail which can be taken off and reseated easily. The soaking boot is more likely to be caused by the high level brake light seal. You can take that light unit out and use use a smear of roofing sealant or similar to make good the seal. The oil leak could simply be damage to the oil filter or sump getting blown about under the car. I doubt it's terminal unless it has run completely dry.
The clutch is a cable jobby with an adjuster on the top rear of the engine. It is a bit of a squeeze to get you hand in the gap but if you're an amateur gynaecologist you'll manage. It doesn't take much adjustment to make a difference but I managed to re-adjust mine back to normal from what I thought was a knackered clutch.
I think your dealer is trying it on.