Translation:Three small ones, please.
Adjective + の(は)
The 'one' that...
な-Adjective + なの(は/も)
い-Adjective + の(は/も)
[の takes the place of a noun that is omitted from the sentence・の turns the proceeding clause/adjective into a noun]
Could be either. の can be used to substantivate verbs, so that 走るのが好きです means "I like [the act of] running", but it is indeed also used to refer to previously mentioned -or contextually indicated- objects. Say you have a few robots; some stand still, some can walk, and some run. Then 走るのが好きです could be taken to mean "I like the running one". More like than not though, the verb would be in present continuous in that case; i.e. 走っているの.
When の is being used like it is in the Duolingo sentence, の just completely replaces whatever noun you were talking about. You would only use の if you and the person you're talking to know what you're talking about. But we don't know with the sentence Duolingo gave us. There's no context. http://www.guidetojapanese.org/particles3.html