"an authority" is a person or institution that has power to do something "authority" is also an abstract noun with a meaning similar to "power" You have to know from context which sense of the word is being used "When I reached the age of 18, my parents no longer had authority over me." "To get a driving licence, you need to apply to the relevant authority." "in town" is an idiom. The meaning is close to "here". It's like "in bed", "at home", or "at school". These are adverbial expressions rather than prepositional ones. In each case, we are not focusing on identifying the particular place where someone is in or at. Either it is known, or it doesn't matter. Rather, we are referring to someone's current status, with a reference to a place. "The gang is back in town and so we can expect some trouble tonight". "He's at school at the moment, but he will be home by 5pm. Come back then."

It seems that this is a crucial problem to your English learning. Native English speakers will give you good explanation. I believe you will know well by intuition when to use and when not to use "the" after you have comprehended this usage of "the".