Learn Russian: Мы закончим делать ароматный букет и возьмём три длинные ленты. - We will finish making the fragrant bouquet and will take three long ribbons.

This is a special rule for feminine nouns like лента. After the numbers 2, 3, and 4 in the Nominative or inanimate Accusative cases, adjectives describing feminine nouns take the Nominative plural form (длинные). If the noun were masculine or neuter, you would use the Genitive plural instead.

Is ленты here in the Nominative plural or the Genitive singular?

It is in the Genitive singular. Although the Genitive singular and Nominative plural forms of лента look exactly the same (ленты), the grammatical rule for the numbers 2, 3, and 4 dictates that the following noun must be in the Genitive singular.

Why do we use the imperfective verb делать immediately after the perfective verb закончим?

Закончить is a phase verb, meaning it describes the beginning, continuation, or end of an action. In Russian, phase verbs are always followed by an imperfective infinitive like делать, because you are stopping an ongoing process rather than a one-time completed result.

Since ароматный букет is the direct object being made, why doesn't it take an Accusative case ending?

It is actually in the Accusative case! Because букет is a masculine inanimate noun, its Accusative form is identical to its Nominative form. The adjective ароматный follows the same rule.