Double Negative.

Just wondering: Is it possible to create a positive image by shooting negative film through a slide duplicator with negative film in the camera?

Yes, it's possible; however, depending on your needs (that is, whether you will print the positives or project them), you may need to alter your exposure and development to achieve a suitable level of contrast.

Yes! This is basically how cine prints are made, because negative is used in cameras. "Positive" film stocks are made for this purpose. They are basically slow (like ISO 1...10), very fine-grained, high-contrast negative films with low fog and are called "print films". There was a color print film for process C-41 for still photography usage, but it has been discontinued. BW print films for still photography are not produced, but you can try some high-contrast, fine-grained slow film (like Ilford PanF plus etc) and develop it in active developer (like a BW paper developer) to a high contrast. Experiment!