Difference between 发愁，着急，担心，关心，操心，烦恼 In addition to this post: Is there a difference between 担心 (dānxīn) and 着急 (zh&#225;oj&#237;)?

HSK contains a lot of words which relate to being worried:
发愁，着急，担心，关心，操心，烦恼
- am trying to distinguish the difference between them. This is what I have so far, which I assume is accurate (please let me know if not!)

发愁 - worried, concerned - but not in an emotional way, Ex: the manager is worried about finding enough qualified staff / the economic situation.

着急 - adj. worried, anxious (optional: that can cause reduction in quality of output). Ex: Mother can't find her kids; (+ optional:) child is about to give a piano recital.

担心 - v. to worry about possible future event, but assume that it won't come to pass - Ex: to be worried about the small chance of not passing an exam.

关心 - v. care, worry in a general sense, i.e. not for a reason that is currently evident - mother worries about her children, i.e. cares for them, likes them, but there is no immediate danger or risk.

However, I am quite unsure about these two:

操心 - Not sure what kind of worry this is and how it can be differentiated from the other entries

烦恼 - v. to be worried, n. worry (emotionally disturbed) - Or does this mean annoyed?

Any help with understanding these would be much appreciated!
Many thanks in advance
发愁 - The things to worry are like huge fruits hanging on their stem. It burdens.

着急 - So worried to urge oneself to "do something!" (at all)

担心 - Concerned about something, say a friend's health. The heart feels like hanging in the air.

关心 - Generally care about something, may or may not to an extent of concerning. (Btw, I so agree with your definition for this one)

操心 - Devote oneself into something, put a lot of efforts or thinking's into, because one cares about it or is concerned about it. For example, a parent may be so worried about the child's study, that they take a lot of efforts to research which school is better, which teacher is better, which major is safer, etc.

烦恼 - It can be both a word or a noun, either "to worry about" or "worry". But the degree of worry can be a bit intense. 烦 means annoyance and 恼 means anger. They together lean more towards annoyance, or generally anything that's mentally disturbing or causes discomfort. Or as a verb, it means staying full of those annoying emotions.