Learn Polish: Masz fajne auto. - You have a cool car.

Because auto is a neuter noun. In Polish, the accusative case is always identical to the nominative case for all neuter nouns. The adjective fajne also matches this neuter nominative/accusative form, so the phrase doesn't change its ending.

Is there any difference between using auto and samochód for "car"?

They are completely interchangeable in everyday speech, but auto is slightly more conversational and informal. You will hear both constantly, but in formal, legal, or official contexts (like a police report or an insurance document), samochód is always preferred.

Since auto is a foreign borrowing, is it an indeclinable noun in Polish?

No, auto declines perfectly normally like a standard neuter noun. While some foreign borrowings ending in "-o" are indeed indeclinable (like awokado or kakao), auto fully changes by case. For example, in the locative case you would say w fajnym aucie (in a cool car), and in the genitive nie mam fajnego auta (I don't have a cool car).

Is the word fajne (cool/nice) acceptable to use in all situations?