Your questions reveal you've done little of your own research. It's always a good idea to read up on the forums because many of these topics have been covered before.
Have a look at this for your skewb question: http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=658
- A skewb is made by using a 4-armed core. It's a shortcut way to skip a full shells mechanism and this can be done because 4 corners are always in the same position relative to each other.
Some puzzles are made by hand and there are plenty of ways to do that. If your puzzle is more complicated and can't be based of an existing one, then usually CAD (Computer Aided Design) is used to make them. First, the puzzle pieces are designed in a CAD program like SolidWorks. They are then 3D printed by a company called Shapeways. You simply send them the 3D Model (STL file) and they will produce the pieces as you've designed them and send you them.
Unfortunately CAD is hard to learn (1-2 years) and 3D printing is expensive (upwards of $150 for one puzzle).