Learn Polish: Naprawiali mój stary samochód. - They were fixing my old car.

Because the sentence means they "were fixing" it, focusing on the ongoing process in the past. To show this continuous action, we use the imperfective verb naprawiać (to fix). If we wanted to say they successfully "fixed" it and finished the job, we would use the perfective verb naprawić and say naprawili.

What does the -li ending in naprawiali tell us about who was fixing the car?

The -li ending tells us that "they" refers to a group that includes at least one male person (the masculine personal gender). If a group of female mechanics was fixing the car, we would use the non-masculine personal ending -ły and say naprawiały.

Which case is mój stary samochód in, and why didn't the words change their endings?

It is in the accusative case because it is the direct object of the verb. However, for masculine inanimate nouns like samochód (car), the accusative form looks exactly the same as the basic dictionary form (the nominative). The words mój and stary simply copy that same form.

What would happen to mój stary if the object was a masculine animate noun, like a dog?