Still a learner of Italian, I am also hesitant about these two. In one context, I used "veramente?!" to mean "are you serious?/really?" and the native speaker corrected me saying "you should use 'davvero', in this sense". So, considering this suggestion, I think "veramente" is rather formal and much commonly used as an intensifier to an adjective, whereas "davvero" functions better by itself, or perhaps even with a verb. And perhaps these link might help us to understand the issue better:
As a Spanish speaker, I can tell you that the word has quite different meanings. "Yo no estoy verdaderamente seguro" (translation of Non sono veramente sicuro), and "Yo no me siento verdaderamente seguro en este lugar" ( I do not feel SAFE in this place). So you can see that we use it as "being sure or not about something", and "feeling or being safe in a place" Italians do the same.
Andrea: "somo" doesn't exist. Wherever you saw that it's clearly either a typo for 'sono' or just an error. "sono" is used for both "I" and "they". Here you know it's "I" and not "they" because of the adjective ending -- sicurO, rather than "sicuri" or if feminine plural "sicure".