Learn Finnish: Kandidaatti kirjoitti esseet ja suoritti tentit. - The bachelor wrote the essays and completed the exams.

You would change the subject kandidaatti to the genitive (kandidaatin), and change the past tense verbs to the past active participle ending in -neen. The phrase becomes: Kuulin kandidaatin kirjoittaneen esseet ja suorittaneen tentit. This efficiently replaces the longer että (that) clause.

Why are the objects esseet and tentit in the plural nominative form (-t) rather than the partitive plural?

Because the actions were fully completed. When an action is finished and affects the whole object (a total object), we use the accusative case. For plural words, the accusative looks exactly like the standard plural nominative ending in -t. If the bachelor was still in the middle of writing them, you would use the partitive plural: Kandidaatti kirjoitti esseitä.

Why doesn't the double tt in kirjoitti and suoritti weaken to a single t through consonant gradation?

In the past tense (imperfect), consonant gradation is triggered by closed syllables. The third-person singular ending consists of just a vowel (-i), which leaves the final syllable open (kir-joit-ti). Therefore, the strong grade tt remains. You would see the weak grade if it were the first person: minä kirjoitin (kir-joi-tin).

Does kandidaatti just mean a job candidate?