One approach to stacks to call a stack a "sheaf of groupoids" which means a functor $$ \mathcal{C}^{\text{op}} \rightarrow \mathcal{G} $$ from a category $\mathcal{C}$ with a Grothendieck topology to the category of (small) groupoids $\mathcal{G}$ ([small] 1-groupoids) satisfying a descent condition.
The usual way of doing this is with $\mathcal{C}:$=$R$-mod, for a commutative ring $R$, with the flat topology, but certainly other choices could be made. I have recently heard that there is a well defined notion of $\text{spec}(E)$ for $E$ a commutative ring spectrum.
Question 1: Is there such a thing as a stack on commutative ring spectra?
Question 2: Can equivariant structure be encoded into the geometry in some way so that this perspective gives you new new tools to work with equivariant homotopy?
Question 3: Are there other uses for this construction in the literature?