Something that is done earnestly is done with deep and sincere feeling. Something that is done solemnly is done in a serious, formal, or ceremonial manner, and perhaps also in a way that is legally binding. This somber adverb conveys a sense of weighty importance, and is overwhelmingly used with the verb swear, as in the U.S. presidential oath of office: “I do solemnly swear that I will faithfully execute the Office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States.”
The noun spunk refers to one’s spirit or pluck and suggests a lively determination. This term has a fiery background, literally, entering English referring first to a spark and then to ignitable wood or tinder. The far less combustible noun gumption refers to courage and guts. It might take gumption, for instance, to quit a high-paying job. It’s not a stretch to say that gumption is more grounded than spunk, since gumption also implies a resourcefulness and even shrewd common sense in solving problems or getting things done.
The nouns fairness and equity both deal with what is fair and just, but equity is more often used in discussions of complex, systemic disparities—and how to solve them. Equity is broadly defined as “the quality of being fair or impartial,” and it is related to the word equal. But be careful not to conflate equity and equality: while the concepts are certainly intertwined, the key idea that sets equity apart is that people's needs and circumstances are different, and therefore solutions must differ appropriately.