As far as I understand your question you want to know what the meaning of adding "green" to various nouns, right?
If that's the case then "green eyed" means jealous. "Green hand" can mean someone who is good at gardening, for example "She has a great pair of green hands in the garden." I believe in American English it can also mean a "novice".. which is the same meaning as "green horn." Unfortunately I have no idea for "green room." Finally for "green power" for my understanding this refers to environmentally and sustainable forms of power, such as solar, wind, wave etc.
I hope that helps!