Lostspark, don’t believe everything you read. If some things you read cause you to question, I suggest you find a knowledgeable, kind Lubavitcher you could trust to discuss these ideas with and hear his thoughts.
An example of a misunderstood fact that you mentioned (among others):
How come the Rebbitzin didn�t wear a sheitl but the Rebbe encouraged all Lubavitch women to do so? How come everyone lies when asked?
This is simply an error.
I just spoke to a guy who would bring the Rebbetzin’s sheitel to a sheitelmacher (Mrs. Kugel) all the time. In later years she had a gray/silver sheitel, and she would wear a tichel partially covering it.
(In the Rebbetzin deposition video, she is wearing this sheitel and tichel, as this man told me � he was present there as well.)