Regarding your question of how Zero was able to materialize on the real world, the explanation is the following:
After the defeat of the Super Cybeast Greizar (on Episode 25 of Beast), the 'Professor' began to rebuild it and upgrade its 'Beast Factor' into the 'Zero Virus'. The Zero Virus upgrade to the 'Beast Factor' allowed Net Navis to materialize at will without Dimensional Areas or Copy Roids. Zero was installed that program, obviously, and that's how it can materialize.
Another example are the Phantom Darkloids created by Cache. They also have the ability to materialize on the real world at will.
Hope this helps answer your questions.