It is eminently possible to teach yourself photography, as there are a vast amount of resources available these days to enable you to do just that. Perhaps a good place to start would be to get a book on general photography techniques, using that to learn the proper terms to search for online. The web has thousands of tutorials and blogs - just search for photography tutorials and browse.

There are no rules to when you can 'call yourself' a photographer. Technically you are a professional photographer once your main income comes from selling your photographs. However, it will probably take a lot of time and practice before you can start taking photos that sell, though this of course depends on how talented you are. I would concentrate on thoroughly learning the basics than thinking about the commercial aspects at the moment.

As for slow motion pictures, by which I think you mean long-exposure pictures, they can be taken with your DSLR and any lens. Read your manual and look for Shutter Priority and Bulb modes, and search the Web for 'how to take long exposure photographs'. The idea is that the shutter is open for a long time, blurring motion.