Learn Hardcore German: Ein Notfall muss der Feuerwehr gemeldet werden. - An emergency must be reported to the fire department.

Ein Notfall is in the nominative case—it’s the subject of the passive clause. der Feuerwehr is in the dative case because the verb melden normally takes a dative object (you report something to someone). In a passive with two objects, the original accusative becomes the passive subject (nominative), while the original dative remains dative.

How can I tell this sentence is in the passive voice?

Passive voice is indicated by the past participle gemeldet combined with a form of werden (here as an infinitive after the modal muss). In active voice you would say „Jemand muss einen Notfall der Feuerwehr melden.“ Passive shifts focus to the emergency itself, not on who reports it.

How do you form a passive sentence with a modal verb like muss?

The finite modal (muss) goes to the second position. The past participle (gemeldet) and werden are placed together at the end. Pattern:
Subject + modal + (other elements) + past participle + werden.

Why is there no preposition before der Feuerwehr? Could I say bei der Feuerwehr?

The verb melden can take a dative object directly (jemand meldet jemandem etwas). So der Feuerwehr is the indirect object without a preposition. You can also say einen Notfall bei der Feuerwehr melden (using bei + dative), which is common in spoken German, but here the bare dative is correct.

Why does die Feuerwehr become der Feuerwehr in this sentence?

Feuerwehr is a feminine noun (die Feuerwehr). In the dative singular, the feminine article die changes to der.

How would I add an explicit agent (“by someone”) in this passive construction?

Introduce the agent with von + dative:
„Ein Notfall muss der Feuerwehr von jedem Zeugen gemeldet werden.“
Here von jedem Zeugen names who should do the reporting.

Can I front the dative object for emphasis? For example: Der Feuerwehr muss ein Notfall gemeldet werden?

Yes. German allows you to move elements to the front for emphasis or topic. If you start with Der Feuerwehr, the finite verb muss still remains in second position:
„Der Feuerwehr muss ein Notfall gemeldet werden.“
The meaning stays the same.

How can I express the same obligation using sein + zu + Infinitiv?

That’s a more formal way to show necessity:
„Ein Notfall ist der Feuerwehr zu melden.“
Here ist is the finite verb, der Feuerwehr stays dative, and zu melden expresses the required action.

How do I turn this sentence into the active voice?

Use an impersonal or specific subject and a normal verb order:
„Man muss einen Notfall der Feuerwehr melden.“
or
„Jemand muss einen Notfall bei der Feuerwehr melden.“
Then the agent and action are explicit.

What changes if I make Notfälle plural?

You switch the subject to plural and adjust the modal accordingly:
„Notfälle müssen der Feuerwehr gemeldet werden.“
Notice Notfälle (pl), müssen (pl), and der Feuerwehr stays the same (dative singular).