What does "Diagnostic-menu" really mean ? 

The diagnostic-menu is a function which is optional in cellular-phones.
Usually you can only turn it on with an undocumented code, often you even need
a special software provided only by the manufacturer (e.g. Nokia).
The diagnostic-function informs you about different net-parameters, for example
the actual broadcast-channel, the actual power-level which is used while telephoning,
the receiving signal-level etc.. The diagnostic-function itself is a passive function,
so you cannot change any net-parameter or damage something with it!
Actually the diagnostic-function-menu is only interesting for technology freaks or for
people who already possess the necessary background information, for example from the
internet (see my referring GSM-link-page) or from referring technical literature.
Sometimes the diagnostic-function is used by a net-provider or its staff.