Spurred by the discovery of a boson resonance at the LHC as the result of the search for the Standard Model Higgs, we pursue our investigation of the properties and signatures of Higgses in an effective supersymmetric scenario that goes beyond the usual MSSM. Such scenarios were first introduced to alleviate the naturalness problem of the MSSM Higgs and are found to have a very rich phenomenology that allows departures from the Standard Model in the production rate of the Higgs in many of the search channels. We now include the constraints from flavour observables in particular the rare decays b-> s gamma and Bs -> mu+ mu- including the recent measurement from LHCb. We also address the issue of Dark Matter and its impact on Higgs physics. In particular, we incorporate the latest data from XENON100 on the spin independent direct detection rates. These turn out to be powerful constraints, especially if one also imposes that the observed thermal relic density is obtained. We also study models with a low abundance that can more easily evade the direct detection rates. We study the impact of the flavour and Dark Matter observables on the production rates of the Higgs at the LHC, and their correlations in the diphoton, diphoton+jets and 4 leptons. We also comment on the other channels.
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