Hi Red O.,
With respect to Gram staining, this is a characteristic used grossly (in the sense of broadly, as opposed to in detail) to divide bacteria according to absorption of certain dye chemicals. You could and should look up "Gram stain" as a search term to learn more detail. Another such gross division is between aerobic and anaerobic species.
Nowadays genomic sequencing, such as 16S rRNA sequencing, is more definitive, though not necessarily faster, for identifying species.
DNA Location: in nucleoid, as generally a single circular molecule.
Protein synthesis location: in ribosomes, just like in your cells.
-- Cheers, -- Mr. d.