If you talk about the American passport you do not have to go to the US Embassy in Romania. Try here https: //travel.state.gov/content/travel/en/passports.html ... If vb of the Romanian passport can be done at the consulate
Yes you can. There is a whole description of the process on the website. You could also get a travel permit and travel to Romania to get your passport cheaper. The application fees and other taxes could be quite costly. Good luck.
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