$$K^0 \rightarrow \mu^+ + \mu^-$$ Just like a neutral kaon decays into a pair of pions, can it also decay into a pair of muons? If not, why?
Yes, this decay is possible, and measured to occur, via diagrams similar to:
involving two W bosons. Note that since it involves one more W boson than the $\rm K^0$ to pion decays, the decay is suppressed pretty strongly.
There are some subtleties involved here regarding CP violation, depending on whether the original particle is a $\rm K^0_L$ or $\rm K^0_S$. But overall this decay can happen.