dictionary forms are used when you restrict to simple narration. they are used quite often. you just have to listen to its context more often then you will know when it is appropriate to use them.

I think it's because 아프다, 무섭다, 예쁘다, 멋지다 are technically adjectives in Korean grammar. If it's hard to accept that these are adjectives, then understand it as 아픈(adjective) + 이다(be verb). You can always say "~이다" in speech or writing as in "Jane은 여자이다." That's why you can say "Jane은 예쁘다." Other than that, you almost never use a dictionary form of verb as "a main verb". However, a dictionary form can be used when it is in a position where a dictionary form is required, like in English you have to use a dictionary form after "want to". '먹다' 먹다(가) 토했다. I was eating but threw up. 먹다(가) 말았다. I was eating but stopped halfway 먹다(만) 음식. food that was left over. '중요하다' 역사가 중요하다는 사실 the fact that history is important 돈이 중요하다더니 아니었다. It was said that money was important but it wasn't true. '행복하다' 그녀는 행복하다고 말했다. She said she was happy. '쓰다' 안경을 자주 쓰다보니 불편하다. It is inconvenient because I wear glasses often.

You can use the dictionary form of the verb only when talking to a child, close friend or yourself. Otherwise, it is not polite at all. You should never use this form when addressing a stranger or a superior (boss, grandparent etc.)