Your Nicca is quite a distinguished Japanese camera. The Nicca company was founded by a group of former Seiki Kogaku (Canon) employees, who started a repair shop and then moved into making cameras; its first camera (sold as the Nippon) appeared in 1942, and the company was in business under its own name until 1958, when it became part of Yashica.
Although the design is based on that of the Leica screwmount cameras, the Nicca is far from a "cheap copy" -- one evidence of this is that they bought their lenses from Nikon, and the 5cm f/1.4 Nikkor with which yours is equipped was one of the best high-speed lenses of its era.
Figuring out exactly which Nicca model you have of the dozen or so variants they made will be complicated by the fact that most of them were fairly similar. If you really want to know exactly which one you have, your best bet probably is to borrow a copy of McKeown's Price Guide to Cameras and identify it based on what features it has.
As to tell how well it works: the bottom-load design (similar to Leicas of the same era) means you can't check the shutter by looking through the back. But you can remove the bottom and slide a white card, such as the back of a business card, up into the film gate; then, unscrew the lens and operate the shutter at all its speeds while looking in through the lens mount. Aim a strong non-fluorescent light, such as a desk lamp, down into the lens mount and watch carefully as you fire the shutter at various speeds. You'll be able to see the white card flash into view as the shutter opens, giving you at least a rough idea of how it's working.
The real test, of course, is to load up a roll of film and give it a try. Operation should be almost identical to that of a Leica IIIc or similar models, so if you can find loading and operating instructions for those (I think there are some here on RFF somewhere) they should be close enough to let you figure out how to operate your Nicca.
If it's in good working condition, it should be an excellent picture-taker!
