1. its a little bit redundant. It means the same without “ㅡㄹ때도 있다” and it goes like 가끔 정말 마음에 드는 옷 가게를 발견한다. 정말 마음에 드는 옷 가게를 발견할 때도 있다. is also okay. 2. 마음에 드는 is like a idiom. 그 차가 마음에 들다 means I like the tea. 3. The answer is the same as number two. 들다 has a lot of meanings but 들다 itself does not mean anything related to like. you can also say 눈에 들다. 4. Korean punctuation says each word(excluding postpositional particle(도,가,이,를,을)) should be separated. Since 때 is a noun it should be separated with 있다.

가끔 (((정말)-> (마음에 드는))-> 옷가게를) ((발견할)-> 때도)->있다 가끔: once in a while 정말 마음에 드는 : that I really like; to my liking 옷가게를: clothing store (object) 발견할 때도 있다: happen to discover Once in a while, I just happen to discover a clothing store to my liking.

Here's some more details. 1. I don't think 가끔 is redundant. "도" in 도 있다 means "also" or "in addition", meaning that it's not something commonplace or the main thing being talked about but there indeed are times that it happens. It doesn't have any notion of frequency. 가끔 adds the sense of "once in a while", and at the same time makes the sentence sound smoother. 2. Yes, 들다's original meaning is to "enter". 마음에 들다 is thus to enter into(에) one's mind (nicely), which is similar to 좋다 or 좋은 느낌/인상을 갖다/받다. Compared with 좋다/좋아하다, 마음에 들다 is slightly more subtle and describes liking a person or thing for the first time especially well. 3. Again, 들다 means to "enter". Its main phrases are 마음에 들다 / 마음에 안 들다 (happen to like or dislike something) and 눈에 들다 (visually/instinctively like something) / 눈 밖에 나다 (fall out of favor with someone). Both 좋다 and 마음에 들다 invert the sentence (i.e. the object of liking becomes the subject), while 좋아하다 has the usually SOV structure. 4. 있다 in the sentence is a conjugated form. For adjectives, of which 있다 is one, the plain -다 conjugation is the same as the base form. - verb examples: 가다(base): 갑니다, 간다, 가요, 가 / 먹다(base): 먹습니다, 먹는다, 먹어요, 먹어. (all distinct) - adjective examples: 넓다(base): 넓습니다, 넓다, 넓어요, 넓어 / 좋다(base): 좋습니다, 좋다, 좋아요, 좋아. (the second -다 conjugation is the same as the base form) This is one of the few cases where adjectives behave differently from verbs in Korean.