It means 'Hello' in an informal way, this is the way you greet your close friends in Korean.

In general, you consider a Korean verb as an action or a process. A Korean adjective usually describes a state of being. I don't think there's another way to identify which is which. I don't know about a dictionary either. 비다 is an adjective, so it's conjugated as an adjective. You cannot say 나는 잔을 빈다, because 비다 means to be empty, not to empty. The verb related to 비다 is 비우다. 나는 잔을 비워요. - I empty the glass. Yes, 빈 잔 means 'empty cup'. I'm not really sure about how it goes with 'a cup which is empty', I think it would be something like 비우는 잔, or 비울 잔 for Future Tense, but these two are actually translated to 'cup which is being emptied (by someone)' and 'cup which will be (being) emptied'. Sorry I couldn't help you more. :)

1. The difference between 하던 & 했던 As far as I know, there's no difference between 하던 and 헤던. I guess both of 'em can be used in the same context, having no change in meaning. Actually, it sounds a little weird and unnatural to use 던 in the present tense, I've never seen it before. Koreans never say ' 내가 하던 일이에요', they say '내가 했던 일이에요'. (That's the work I did) 하다(present tense) + 던 = 하던 - Almost never used in every day speech, maybe in some kind of dialect. 했다(past tense) + 던 = 했던 - Sounds more natural. 2. The difference between 했었어 and 하던 Well, the former one is the Past Perfect tense of Korean language. Expresses a past occurrence that doesn't continue to the present. 현우 씨는 작년에 한국에 왔았어요. (Hyunwoo came to Korea and later left; he is not in Korea now) The latter one has already received an explanation. You cannot compare those two because they're different grammar points, one can never replace the other. 3. 은/ᄂ and 했던 in forming adjectives in the past I don't know what you actually need an explanation for... 내가 가는 곳이에요. - That's the place I go to. (는 particle, used to form adjectives related to present actions) 내가 갔던 곳이에요. - That's the place I went to. (았던/해던, used to form adjectives related to past actions)