Can you bring food like sausages raw and cooked, fish in packaging etc. from Germany with via plane?

In Germany visiting my in laws at the moment and wonder if I can bring those food mentioned back with our flight. Rekon it is under the same EU regulations but just want to be sure.

Also: my father-in-law hunt, can you bring product like ham, sausage that he made from the game meat? I suppose not because it is not a registered product?

Thanks to all the help!