어느 추운 겨울에 호랑이가 숲 속을 다녔어요 is fine. It's using the soft, polite style prose which is common for children's books (adult books use the -다 ending though). 없은니? in the second sentence is wrong. It should be 없니? if you want the -니? question ending. But the overall description gives the impression that the tiger is talking to himself, i.e. wondering out loud. if so, you would use -나? or -ㄹ까? which is for that. 없니? is for asking someone, and it sounds strange because there is only one character. Speech style involves politeness, formality, and showing respect - it is more than just formal versus informal. There is a set of sentence endings to express politeness/formality, and there are "honorific" verb forms which express respect. The sentence endings change the register of the speech to the person you're talking to. Here's a summary of the four distinct styles, based on present tense 가다(verb) and 슬프다(adj) example. 1. -ㅂ니다: 갑니다, 슬픕니다. (polite and formal when used in writing, talking to a group, in broadcasting, etc) 2. -다: 간다, 슬프다. (impersonal in writings, familiar in speech) 3. -아/어요: 가요, 슬퍼요. (polite - the most common speech form between adults) 4. -아/어: 가, 슬퍼. (familiar - between close friends, or when talking to children) (New learners can get by with the polite style of #3 for all situations.) An honorific form of a verb shows respect to the subject of the verb, i.e. the person mentioned in the sentence, which is not necessarily the same as the listener. 1. 영철아, 선생님이 못 오신대 (= 못 오신다고 해) = 영철, they say the teacher can't come. 2. 선생님, 빨리 오세요. = Teacher, please come quick. In #1, the ending is in familiar form (#4 above) as the speaker is talking to their friend, but it's using the honorific form 오시다 instead of plain 오다 because they want to be respectful to the teacher being mentioned. In #2, the speaker is talking to the teacher, so they're using the polite ending -아/어요 as well as the honorific form 오시다 (오시다 + -아/어요 -> 오시어요 -> 오세요).

thanks alot @kun kim

Honestly, I believe it would be really hard for non-native speakers to use formal grammar correctly. The simplest rule to remember is that formal one usually followed by 요, but it is still quite complicated because it changes a form of the sentence. For example, 어느 추운 겨울에 호랑이가 숲 속을 다녔어요,(which is you posted ), this is in formal form. you can see 요 at the end right? you can switch this into informal by deleting and changing form of the end. 어느 추운 겨울에 호랑이가 숲 속을 다녀왔어. this is an inform form. The latter sentence, "배가고픈데 뭐 먹을 것이 없니?" is in informal form. you can change this to formal one by adding 요 and changing the end of sentence. 배가 고픈데 뭐 먹을것이 없어"요"? I understand this is quite complicated, and as a native speak, I do not know what kind of rules applies.