Can the method and the products manufactured by this method be patented at the same time in the invention patent?

Of course. This is called a joint application. If authorized, they must be single. If it is not a single one, you need to delete one, and you can apply for a divisional application for the deleted part. If you want to know more, I suggest you look at the single explanation. If in doubt, please add QQ 12 1849468.