Yes, when in doubt, delete everything and restart. It goes without saying that when one has 20 or 30 precompiled Julia libraries, this is not something I look forward to. What a waste of time!! I do appreciate your reply. Atom and associated software, including Julia, have a long way to go before they achieve the robustness (or perceived robustness) of Python. But I do like the language (Julia).
Problem solved: I followed your advice. I deleted ink, remote-edit, remote-edit-2, julia-client, which were mentioned in the errors posted above. I then reinstalled them, quit, atom, and relaunched. All icons are back. Precompilation of all my libraries was instantaneous!! What a great feeling! Thank you so much for the approach, @Ahmed_Salih.