Learn Hardcore Polish: Podczas awarii trzeba naprawić zepsuty przycisk na panelu. - During the breakdown it is necessary to repair the broken button on the panel.

Podczas is a preposition that always takes the genitive case. The noun awaria (nominative) changes to awarii in the genitive, so you get podczas awarii (“during a breakdown”).

Could I say w czasie awarii instead of podczas awarii?

Yes. W czasie awarii also means “during the breakdown.”

Podczas is a single-word preposition often used for specific events.
W czasie is a two-word phrase that’s slightly more formal or descriptive but equally correct here.

Why is there no explicit subject in this sentence? What role does trzeba play?

Trzeba is an impersonal modal verb meaning “one must” or “it’s necessary to.” It never has a personal subject; the person is general/unspecified. After trzeba, you always use an infinitive.

Why is the verb naprawić in the infinitive form and not conjugated?

Because trzeba requires an infinitive. You say trzeba naprawić (“it is necessary to fix”) rather than naprawisz or naprawia.