Mostly correct! Some of the weirdness with counting comes out, too - their language has a base nine counting system, not a base ten, and the weirdness with the plurals was that they have a separate form for 'one [noun],' 'two [nouns],' and 'three [nouns],' and instead of a set plural form after that, the first three forms repeat - so 'four [nouns]' and 'seven [nouns]' both use the 'single' form for the noun, while 'five [nouns]' and 'eight [nouns]' uses the dual, and 'six [nouns]' and 'nine [nouns]' use the triple. (An unspecified number of things always uses the triple form, which is the simplest and is what umbreon gives when asked about the word for a noun.)
Words for negation are apparently kind of complex, but the word the umbreon used for Ellie was pretty much 'not an eevee,' and the counting song was in fact counting eevees - umbreon says 'nine eevees' a couple times, slowly and broken up into word parts, until it becomes apparent they share a root.