The use of dom vs. domsa is simply one of emphasis. Usually it would just be “dom” but you can say “domsa” if you want to emphasize that you’re the one you’re talking about.
Yeah, that makes sense. If one person says they’re from one place, the other might answer with the emphatic form to draw contrast, like in English if one person said “I’m from Boston” and the other person answered “Well, I’m from New York”.