Learn Russian: Дирижёр управляет оркестром подобно капитану корабля. - The conductor controls the orchestra like a captain of a ship.

The preposition подобно ("like" or "similar to") strictly requires the Dative case. It introduces its own prepositional phrase, so the noun immediately following it takes the Dative, completely independent of the cases used in the rest of the sentence.

Could I use как instead of подобно in this sentence?

Yes, you could say ...как капитан корабля. However, подобно is more formal, literary, and poetic. While как simply means "like" or "as" (and would take the Nominative case here to match the subject дирижёр), подобно literally means "similarly to" and strongly emphasizes the exact manner in which the action is performed.

Why is the direct object оркестром in the Instrumental case instead of the Accusative?

The verb управлять (to manage, direct, or steer) is a verb of control, and these verbs require their object to be in the Instrumental case. You will also see this rule apply to similar leadership verbs that you learned earlier, such as руководить (to lead) and командовать (to command).

Is the word подобно related to a regular adjective?