A China company applied for a patent for product A. Our company produces product A in China, but sells it abroad. Is this legal?

According to the patent law, it is an act of patent infringement to manufacture, use, promise to sell, sell or import patented products for production and business purposes without the permission of the patentee. So your sales in other countries are not infringing. The point is that you are still producing (that is, manufacturing) in China, which infringes other people's patents.