Learn Finnish: Kokenut kelloseppä osti nämä vanhat rattaat varaosiksi. - The experienced watchmaker bought these old cogwheels as spare parts.

This is the translative of intended purpose. While the translative case often shows a change of state (becoming something), here it expresses what something is meant to be used as. The watchmaker bought the gears to use them as spare parts (varaosiksi).

Why is the object nämä vanhat rattaat (these old cogwheels) in the nominative plural form rather than the partitive?

Because the action is complete and the object is a specific, whole quantity (a total object). When a total object is in the plural, it takes the nominative plural form (ending in -t). If he were just buying an undefined amount of old cogwheels, it would be in the partitive plural (näitä vanhoja rattaita).

Kokenut looks like a past tense verb form. How is it functioning here?

It is the past active participle (the NUT-participle) of the verb kokea (to experience). At this level, you will often see these participles used just like normal adjectives. Here, it simply acts as an adjective describing the watchmaker.

How is the word varaosiksi formed from its root words?