Learn Finnish: Korkein kaari olisi viimeistelty eilen. - The highest arch would have been finished yesterday.

In the conditional perfect passive, the auxiliary verb is always the active third-person singular conditional form, olisi. The passive voice is carried entirely by the main verb's passive past participle, viimeistelty.

Since "the highest arch" is the thing being finished, why is korkein kaari in the nominative case rather than the partitive?

In Finnish, when an action is fully completed on a whole object in a passive sentence, the object takes the basic nominative case. Because the arch "would have been finished" (a complete action), it is korkein kaari. If the action were incomplete or ongoing, it would use the partitive case (korkeinta kaarta).

The verb viimeistellä (to finish) looks like it comes from another word. How is it formed?

It is derived from the word viime (last) or viimeinen (final). The suffix -tellä is often used to create verbs that mean doing something in a continuous, careful, or focused way, so viimeistellä means "to put the final touches on" or "to finalize" something.

How is the superlative korkein formed from the adjective korkea (high)?

To form the superlative, you start with the basic stem of korkea, which is korkea-. When adding the superlative marker -in, the final -a of the stem drops out, giving us korkein.