Learn Portuguese (Portugal): De acordo com o mito, o extraterrestre estaria a morar na cave. - According to the myth, the alien was allegedly living in the basement.

This is the evidential conditional (condicional de rumor). By using estaria instead of estava, the speaker is distancing themselves from the truth of the statement. It indicates that this is unverified information, hearsay, or a rumor. In English, we often translate this usage by adding words like 'allegedly' or 'reportedly'.

Could we just say moraria instead of estaria a morar?

You could, but it changes the aspect slightly. Estaria a morar emphasizes an ongoing action ('was allegedly living'), whereas moraria translates closer to a simple past statement ('allegedly lived'). The continuous form paints a clearer picture of the alien actively residing there during that time.

I've seen the word porão used for basement. Why does this sentence use cave?

In European Portuguese, cave is the standard, everyday word for the basement or cellar of a building. Porão is primarily used in Portugal to refer to the cargo hold of a ship or airplane. You likely saw porão because it is the standard word for a house's basement in Brazilian Portuguese.

Can I use segundo instead of de acordo com in this sentence?

Yes, absolutely! Segundo o mito means the exact same thing and is highly natural. Both expressions are perfect setups for the evidential conditional because they introduce information that is sourced from somewhere else rather than stated as a firsthand fact.