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. :)