I can try, but the sentences are very close to identical in meaning in English:
Saanko lainata kelloa?
May I borrow a watch (temporarily)?
Saanko lainata kellon?
May I borrow a watch? (I want to take it into my posession.)
The difference is very subtle, and doesn't even necessarily carry any difference in intention. But using accusative in the latter sentence does imply completing one action surrounding the entire clock, and with a verb like lainata, this would imply that you take the clock into your posession (instead of just glancing at it while it's still on the other's wrist). So there is implication that you might take the clock for a longer time, or further away, perhaps for the span of some event you would use it in:
Voinko lainata kellon pääsykokeen ajaksi?
Can I borrow a watch for the duration of the entrance exam?
Also, when talking about borrowing a book from the library, it is preferrable to use accusative, because the book is taken into your posession and out of the library for a longer time, and it's an action that is perceived as concludable:
Lainasin kirjan kirjastosta.
I borrowed a book from the library.
But otherwise, partitive would in general be more usual to use with lainata, because of the nature of that action (temporary, doesn't consume the item).
So it's not really about the number of items, rather about the perceived nature of the action and its uniqueness. This is one of the trickier features of Finnish, so I hope my explanation made some sense.
Vapaampi is not unfinnish sounding, but note that if you are talking about time (which is an unquantified substance) then it needs to be in partitive: vapaampaa. If you talk about yourself, you can say vapaampi:
Minulla on vapaampaa (aikaa) aamuisin.
Minä olen vapaampi aamuisin.