Translations are entered manually and it's not always possible to remember every single one of their variations. This one has been added now.

Because it is tedious for the Duolingo staff to enter in all of the possible variations of each sentence. Just know indefinite article is not needed unless it is necessary to specify a number of something.

In this sentence, for instance, your dad cannot be two doctors, so "one" is understood and usually omitted.

Nope ;)