Can I apply for two patents for an invention?

Of course. An application for a patent for invention or utility model shall be limited to one invention or utility model patent. However, if our invention belongs to the general inventive concept of two or more inventions or utility models, it can be used as an application. An invention, which applies for a patent for a product and a method respectively, has different protection objects. So you can apply for product invention and method invention patent at the same time.