A subset of blazars emit TeV gamma rays which annihilate and pair produce on the extragalactic background light. We have argued in Broderick et al. (2011, Paper I) that plasma beam instabilities can dissipate the pairs energy locally. This heats the intergalactic medium and dramatically increases its entropy after redshift z~2, with important implications for structure formation: (1) This suggests a scenario for the origin of the cool core (CC)/non-cool core (NCC) bimodality in galaxy clusters and groups. Early forming galaxy groups are unaffected because they can efficiently radiate the additional entropy, developing a CC. However, late forming groups do not have sufficient time to cool before the entropy is gravitationally reprocessed through successive mergers - counteracting cooling and raising the core entropy further. Hence blazar heating works different than feedback by active galactic nuclei, which balances radiative cooling but is unable to transform CC into NCC clusters due to the weak coupling to the cluster gas. (2) We predict a suppression of the Sunyaev-Zeldovich power spectrum on angular scales smaller than 5 due to the globally reduced central pressure of groups and clusters forming after z~1. (3) Our redshift dependent entropy floor increases the characteristic halo mass below which dwarf galaxies cannot form by a factor of ~10 (50) at mean density (in voids) over that found in models that include photoionization alone. This prevents the formation of late forming dwarf galaxies (z<2) with masses ranging from 10^{10} to 10^{11} M_sun for redshifts z~2 to 0, respectively. This may help resolve the missing satellite problem in the Milky Way and the void phenomenon of the low observed abundances of dwarf satellites compared to cold dark matter simulations and may bring the observed early star formation histories into agreement with galaxy formation models. (abridged)
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