Can I apply for a utility model patent and a design patent for the same product? In other words, I want to apply for two patents for the same product. I don't know if I rushed them.

You can apply at the same time. Utility model and design are different patents. The utility model protects the shape, structure and connection. The protection points of appearance, color, pattern and combination protected by the design are different, and there is no conflict, but you must ensure that your design will not be copied.