Learn Finnish: Tämä paksu öljy ei sovi näihin pieniin rattaisiin ollenkaan. - This thick oil does not suit these small cogwheels at all.

Since this lesson is about the translative case for intended purpose, why does sopia take the illative (näihin pieniin rattaisiin) here instead of the translative?

While the translative is often used to show what something serves as (like sopii lahjaksi, suits as a gift), the verb sopia takes the illative case (mihin) when talking about fitting into a physical space or suiting a specific object. Here, the oil is physically going into the cogwheels, so we use the illative.

How do we get the illative plural form rattaisiin from the basic word for cogwheel?

The basic form is ratas. For words ending in -as, the stem undergoes reverse consonant gradation (a single t becomes tt) and ends in a long vowel: rattaa-. To form the illative plural, we add the plural -i- and the plural illative suffix -siin, giving us rattaisiin.

Why does the pronoun tämä (this) become näihin here?

Demonstrative pronouns must agree in case and number with the noun they modify. The stem of tämä changes irregularly to nä- in the plural. Adding the plural -i- and the illative -hin gives us näihin (into these), which matches the case of rattaisiin.

Is the adverb ollenkaan (at all) only used in negative sentences?