Learn Spanish (Latin America): Dudábamos que el castigo fuera justo.

The main verb, dudábamos (we doubted), expresses doubt. Expressions of doubt require the subjunctive mood in the following clause. Because the doubting happened in the past, the second verb must be in the past subjunctive (also called the imperfect subjunctive). That's why we use fuera instead of a normal past indicative tense like era or fue.

Is fuera from the verb ir (to go) or ser (to be) in this sentence?

Here it is ser (to be). The past subjunctive forms for ser and ir are identical (fuera, fueras, etc.), just like they are in the preterite tense (fui, fuiste). You can tell them apart by context: describing a punishment as fair (justo) requires "to be," so we know it's ser.

Why do we use ser (fuera) instead of estar (estuviera) for the punishment being fair?

We use ser because being fair (justo) is treated as a core, defining characteristic of the punishment. Remember that estar is used for temporary conditions, emotions, or locations, but whether a punishment is fundamentally just or unjust is an essential quality, which always takes ser.

Why is the main verb dudábamos in the imperfect tense rather than the preterite?