My understanding of this is that the ring is caused by dissemination of the Lyme spirochetes (Borrelia) through the skin out from the initial site of infection.
I agree that the clear area seems a bit mysterious, but I have always assumed by analogy to fungal rings (e.g. Tinea corporis [ringworm]) that it represents areas where the bacteria have been ...
Another example where coinfections are common is with tick-borne illnesses.
One 2006 review suggests that in some regions of North America the prevalence of Ixodes ticks carrying two pathogens may be up to 28% and that from 4-45% of humans with Lyme disease also appear to have ehrlichiosis or babesiosis(Coinfections Acquired from Ixodes Ticks).
While you’re correct that NK cells are often activated (in part) by the absence of MHC-I, they require other signaling events to become fully activated:
The Molecular Mechanism of Natural Killer Cells Function and Its Importance in Cancer Immunotherapy. Paul & Lal. Frontiers in Immunology. 2017.
Activating Receptors on NK Cells
Lack of MHC ...
Depending on the precise details of the experiment, I don't see a particular reason to suppose that being coated with IgA should mean that they'll elicit an IgA response.
I'm assuming that the "coating with IgA" means that the IgA is binding like an antibody, through the variable region binding site on the antibody to some epitope(s) on the bacteria. The ...