Learn Farsi: خواننده از قبل تهدید شده بود.

The phrase shode bud is the past perfect form of the verb shodan (to become/to be). When you combine the noun tahdid (threat) with shode bud, you get the past perfect passive. If it were just "was threatened" (simple past passive), it would be tahdid shod.

Could I use ghablan instead of az ghabl in this sentence?

Yes, you could use ghablan (previously) and the meaning would be almost exactly the same. az ghabl literally means "from before," and it is very commonly used with the past perfect tense to emphasize that an action had "already" happened before another event in the past.

How is the word khaanandeh (singer) formed?

It is made by taking the present stem of the verb khaandan (to read/to sing), which is khaan, and adding the suffix -andeh. This suffix turns a verb stem into a "doer" noun, so khaanandeh literally means "singer" or "reader".

If I wanted to say who threatened the singer, how would I add it to this passive sentence?

In Farsi, true passive sentences rarely mention the "doer" (agent). Unlike English where you can easily say "had been threatened by the manager", Farsi strongly prefers to switch the whole sentence back to the active voice if you want to mention who did it. You would use this passive structure precisely because the person who made the threat is unknown or unimportant.