I think it would be really helpful to have a "Tips" section on this module explaining the use of partitive, since I (and I imagine quite a few others) have never even heard of partitive case before. From the exercises, I sort of get why one would use the partitive for some nouns, but I'm wholly baffled by why it gets used in some cases for adjectives but not in others. Please help us out here.
No, any amounts and any number higher than one triggers partitive singular. If you've heard something about "unspecific" or "indefinite" amounts triggering partitive, that most likely refers to situations where there is no word that expresses an amount but there is a mass noun, for example "meillä on maitoa".