πόδι means both "leg" and "foot". It doesn't differentiate between the two - it includes both. I believe it's the most commonly-used term to refer to either part of the body.
Here's my understanding of the other words:
- σκέλος does indeed mean leg (without the foot)
- κνήμη is shin, so is just a part of the leg
- πους is just the Katharevousa form of πόδι and therefore also includes the foot
- πρόποδες is more like a figurative use of foot, as in 'the foot of the mountain'
A native speaker might want to correct me though.
Thinking his foot was thin/fine/delicate, I heard and wrote ψιλό, which was rejected as a typo. Is this just one of those cases where DL can only countenance one correct answer -- or was my supposition really not possible here? (At any rate, even if only one understanding is accepted in a "Type what you hear" exercise, I still think my hearing easily makes more sense than "one long leg"!)
Unfortunately listening exercises are not independent and will mark correct only the sentences encountered throughout the course. In any case, here you're referring to a body part, so the correct adjective would be "λεπτός". Yes, "ψιλός" means "thin" as well, but it can't be used as freely. The most common collocation is "ψιλή βροχή"=ψιλόβροχο=drizzle.