In order for you to have a dual citizenship, the other country you are a citizen of must also allow this.
You must always check whether the country you are a citizen of accepts that you get a dual citizenship, or whether you will lose your citizenship automatically if you become a Norwegian citizen. You must check this with the authorities in this country, for example through an embassy.
In principle, as a Norwegian citizen, you are obliged to serve your military service in Norway, but the rules vary depending on which other country you are a citizen of. If you have questions about military service, you can contact the Norwegian Armed Forces (external website).