Learn Italian: Che abbia falsificato l'alibi? - Could he have forged the alibi?

This is an independent subjunctive clause. Starting a sentence with Che followed by the subjunctive is a common way to express a deep suspicion, disbelief, or a rhetorical question. It translates best to 'Could it be that...' or 'Is it possible that...' rather than a standard yes/no question.

Why is the past subjunctive (abbia falsificato) used here instead of the present subjunctive?

The past subjunctive is used because the action you are doubting or wondering about (forging the alibi) already took place in the past. If you suspected someone of currently doing something, you would use the present subjunctive, like Che falsifichi le firme? (Could he be forging the signatures?).

Since abbia can be used for I, you (formal), he, or she, how do we know this means 'he'?

The subjunctive forms for the first three singular persons are identical, so context is key. In a real conversation, the speakers would already be discussing a specific suspect. If there were any risk of confusion, you would simply add the pronoun: Che lui abbia falsificato l'alibi?

How does the word alibi work in the plural?

Because alibi is a word of Latin origin that ends in an unstressed -i, it acts like a foreign loanword and is invariable in Italian. The plural form is exactly the same, so 'the alibis' becomes gli alibi.