Learn Russian: ФСБ забрала твой компьютер.

Grammatical gender for indeclinable initialisms is determined by their core noun. ФСБ stands for Федеральная служба безопасности (Federal Security Service). The core word is служба (service), which is feminine. Therefore, the initialism itself acts as a feminine noun, requiring the feminine past-tense verb забрала.

How exactly is ФСБ pronounced aloud?

It is an initialism, meaning you read the name of each letter individually rather than trying to read it as a word. In Russian, it is pronounced as [фэ-эс-бэ].

Why use забрала here instead of another word for "took" like взяла?

While взять means "to take" in a general sense (like picking something up), the prefix за- in забрать specifically means to take something away, often permanently or forcefully. In the context of the authorities taking your belongings, забрать translates perfectly to "confiscated" or "seized".

Are твой компьютер in the nominative case here?

No, they are in the accusative case because they are the direct object being taken. However, because компьютер is a masculine inanimate noun, its accusative form is identical to its nominative form. The pronoun твой follows the exact same rule.