“In the famous picture of her, which is on the official Chabad website, she’s not wearing a sheitel.”
How would you know that from seeing a picture? Because she has a hat with hair protruding? The Minhag in Beis HaRav was to wear a hat on top of the Sheitel, and I see no reason to believe that the Rebbetzin was any different to her predecessors.
“And what do you mean that hardly anyone saw her? Wasn’t their house open with constant streams of people as is the case with Gedolim, great rabbeim and people who live for the kehilla? Didn’t they have hundreds of shabbos guests? Didn’t the females who where desperate for Brachos and chizuk find a place at her door?”
No.
The Rebbetzin was an extremely private individual, and there were no streams of people coming through her home. The only times streams of Gedolim came through the Rebbes own home was when he was sitting Shiva. Gedolim visited the Rebbe in 770, whether for Yechidus, or in the later years, for Dollars. If you are so interested, you can listen to audio and watch video of many of those visits. One particularly well known audio is the visit of the Belzer Rebbe. But it seems from your tone that you are being sarcastic, and trying in intimate that if the Rebbe didn’t have throngs of people streaming through his home obviously he didn’t “live for the kehilla” as did other Gedolim, totally ignoring the fact that the Rebbe spent most of his time in 770, and that’s where countless individuals met with him, Gedolim or simple folk.