Learn Russian: Аппарат может взорваться во время запуска.

The lesson is about using the imperative as an 'if' clause. How could we rephrase this into a hypothetical 'If the vehicle explodes...' using that structure?

You would use the perfective imperative form: Взорвись аппарат во время запуска... (If the vehicle were to explode during launch...). Using the imperative like this makes the hypothetical scenario sound more dramatic or unexpected.

Why does the verb взорваться end in the reflexive particle -ся here?

The base verb взорвать is transitive, meaning to blow something else up. Because the vehicle itself is exploding (it is not blowing up another object), you must use the reflexive -ся to make the verb intransitive.

Why is аппарат translated as 'vehicle' rather than 'apparatus'?

In Russian, аппарат is frequently used as shorthand for летательный аппарат (aircraft) or космический аппарат (spacecraft). In technical or aerospace contexts, 'vehicle' is the most natural English equivalent.

What case is запуска in, and what triggers it?

It is in the genitive case because it directly follows the phrase во время (during). The phrase во время acts as a compound preposition that always forces the following noun into the genitive case.