Learn Farsi: اگر آن‌ها داده‌ها را بازیابی نکرده بودند، سرور خراب می‌شد. - If they had not recovered the data, the server would have been ruined.

In the past perfect tense, the negative prefix na- always attaches to the past participle, never to the auxiliary verb budan. So it becomes nakardeh budand, not kardeh nabudand. Because the verb here is the compound bāzyābi kardan (to recover), the na- goes directly onto the verbal part, giving us bāzyābi nakardeh budand.

Why is the past continuous verb 'mishod' used to mean 'would have been ruined'?

In Farsi, third conditional sentences (talking about unreal situations in the past) use the past perfect in the 'if' clause, but they use the past continuous (also called past imperfect) in the result clause. So kharāb mishod, which normally means 'was breaking' or 'used to break', is actually the standard grammatical way to express 'would have broken' or 'would have been ruined' following an agar clause.

Is 'dādeh-hā' treated as plural in Farsi even though 'data' is usually treated as an uncountable mass noun in everyday English?

Yes, exactly. The root word is dādeh (a piece of data). In Farsi, 'data' in a computing or scientific context is treated as a plural countable noun, so it takes the plural suffix -hā to become dādeh-hā. We also add rā right after it because 'the data' is the specific, known direct object that was not recovered.

Could I drop the pronoun 'ān-hā' (they) from the beginning of the sentence?