What happens to the molecules of the pathogens after phagocytosis? For example, what happens when a bacterium gets digested by a macrophage? I suppose that the macrophage produces the presented antigen from leftovers from the digested bacterial particles. What happens to the rest of the bacterium? Can the molecules from bacteria be used as a source of nutrients for the body? Or will they accumulate/get transported as waste products?

The ingestion of a bacterium by a macrophage involves phagosome lysosome fusion, which you can read about in Abbas Basic Immunology, Ch 2. As you suspected, in addition to bacterial killing and antigen processing, the phagolysosome breaks down bacterial macromolecules, as any lysosome does, using a variety of lysosomal hydrolases. There are export pathways for the end products, including lipids, carbohydrates, and amino acids, as discussed in this review, which does allow for re-use by anabolic pathways. As discussed in the linked review, the process of digestion and catabolite export is regulated, as should be expected. In culture models, nutrient availability appears to be important.