Cadmium is used to control curve shape (contrast) in many chloro bromide and bromide emulsions. It is used in trace amounts, and can be safely used this way, but in large operations such as Kodak or Fuji, are an environmental problem.
Cadmium was removed from all Kodak products in the 60s.
A bromide formula such as the one above should keep several months in the refrigerator and not go into fog. I have kept one that is very similar for months with no problem and no antifoggant or stabilizer. I did have thymol in it to prevent mold and fungus growth.
Unless it is finished with sulfur, it will not perform in any suitable way as an enlarging paper but with sulfur, there will be a very large increase in speed and contrast. Once finished with sulfur, the emulsion should be used immediately unless a stabilzer is added.
Washing is not necessary provided the right formula is used and provided the right final ingredients are added.