Thank you for your enquiry.
For those born abroad, they would be British if born before 1 January 1983 and his or her father was born in the UK (or adopted in the UK by a UK citizen father) or his or her father was registered or naturalised as a British citizen in the UK before the child’s birth. (‘Father’ prior to 1983 means a man legally married to the child’s mother); Mothers could not pass on citizenship before 1983 but there is provision for children of British mothers to be registered.
The Home Office would have said "cannot automatically pass on her British citizenship to her children born abroad". If your grandparents where British citizens otherwise by decent (not by decent) and there is sufficiently strong link with the UK looking back across generation, it would be unfair to deny British citizenship.
It sounds to me that the evidence you may have presented was not sufficiently clear to the Home Office about your case as they do have the discretion to register an adult. You can apply as many times to register as British. But failing this option, you may be able to apply to naturalise as a British citizen under EEA regulations as you are a German citizen and presumably been working in the UK for over 6 years.
Yes your mother will be British by decent because she was born abroad to British parents. The definition of decent comes from the fact a person is born "abroad" to British parents. If your mother was born in the UK she would have acquired British citizenship otherwise by decent.
If you applied under the wrong section then obvious your application will fail. What section did you put down on your form?