You just have to save your templates in SVG, and open the file with Illustrator. Normally, it should work.

The pen tool and the various shapes tools (rectangle tool, ellipse tool, etc) are the only tools you need when you start. If you don't see the tool window, just go in Windows - Tools. This window contains almost everything that you need for now. In the Stroke window, you can change your line thickness and whether the lines and shapes end in a rounded point or not.