Learn Russian: Я закрыл эту вакансию, хотя мы не нашли менеджера. - I closed this vacancy, although we did not find a manager.

Yes! In Russian, you must put a comma before a word that starts a new clause (a part of a sentence with its own subject and verb). Since хотя connects the main sentence to the "although" part, it requires a comma.

Why is it эту вакансию instead of эта вакансия?

It is in the accusative case because it is the direct object of the verb — it is the thing being closed. The feminine word эта (this) changes to эту, and the noun вакансия changes its -я ending to -ю.

Why are the verbs закрыл and нашли in the perfective aspect here?

Both describe single, completed results in the past. The speaker successfully completed the one-time action of closing the vacancy (закрыл), and the team's search for a manager resulted in a final failure to find one (не нашли).

Why does менеджер have an -а at the end (менеджера)?

Because менеджер is a living person (an animate masculine noun), its accusative case looks exactly like its genitive case, adding an -а. Additionally, the direct object of a negative verb like не нашли is often put in the genitive case anyway. In this sentence, both rules lead you to the exact same spelling: менеджера!