Will method claims receive the same priority date if they are filed after product claims are filed first, or can there be a combination of both in one patent application?
One patent can have both method and product claims. Method claims can be how to use it, how to make it and also a method a product executes when activated.
However, a priority filing that doesn’t explain a method is not valid priority to a claim for that method. Each claim must have support in the specification or a priority filing.
Also, an examiner can issue a restriction requirement that tries to separate out either product or process claims. You can fight it and often win, or let one type be examined and try to bring the other type in later, or (in US) file a divisional application to pursue the other claims.