Learn Swedish: En ny strålkastare måste beställas.

This is the passive infinitive. After a modal verb like måste (must), you use the infinitive form. But because the headlight isn't doing the ordering—it is being ordered—you make it passive by adding an -s to the active infinitive beställa.

Can I rephrase this to avoid the passive voice?

Yes! If you want to use the active voice, you just need to add a subject (someone doing the ordering). For example, you could say Man måste beställa en ny strålkastare (One must order a new headlight) or Vi måste beställa... (We must order...).

How do I know whether to use ny or nytt for "new"?

It depends on the gender of the noun it describes. Strålkastare is an en-word (en strålkastare), so the adjective takes the basic form ny. If it were an ett-word, like ett däck (a tire), you would use nytt instead (ett nytt däck).

Strålkastare ends in -are, which usually means a person (like lärare). Is that an exception?

Not exactly! The suffix -are means "a doer" or "a thrower" (from the verb kasta, to throw). While it often refers to people, it is also used for tools or machines that "do" a specific action. A strålkastare literally means a "beam thrower" or "ray thrower".