The Higgs boson mass significantly constrains the available parameter space of many supersymmetry theories. But, there isn't a really good compact way of describing that impact because there are so many versions of SUSY and so many free parameters in the theory.
It really has no obvious impact on theories of multiverse which really don't deserve the title of "theories" anyway.
#3
Ok. Thank you so much. I still have a lot to study.
The most interesting (for me, can't speak for others) consequence of measured Higgs boson mass value is a few unexplained correlations:
With measured top and Higgs masses, SM sits right on vacuum stability/metastability line.
Sum of squares of all SM bosons' masses is equal to half of square of Higgs VEV to within 0.35%.