Can an invention patent be applied for a method and the products manufactured by this method at the same time in one application?

As long as the necessary technical characteristics exist between the two, they can apply together.

There can be two independent claims in the claim, that is, an independent claim for a method and an independent claim for a product. Each independent claim can be followed by a dependent claim.

Accordingly, the description must be consistent with the claims.

Supplement: A dependent claim should be written next to the independent claim it refers to, and then another independent claim should be written.