My mother who is now deceased was born in Germany. She obtained American citizenship. Is there any chance that I can obtain a German passport?

Germany does not recognize dual citizenship. If she became naturalized before you were born, the answer is no... but if she was a green card holder by the time you were born, maybe... but if she never reported your birth to the German embassy, it's now too late.

The father of my son is a german born. I am a kenyan born. Is it applicable for my son to obtain a german passport?