The higgs boson is an elementary particle so how it can decays into another elementary particle; the photon? And why the photon doesn't interact with the Higgs field?
The photon implements the electromagnetic force - it interacts with charged particles. Because the Higgs boson is neutral, it cannot (directly) interact with the photon.
Another reason why the Higgs boson and the photon cannot (directly) interact is that interactions with the Higgs boson result in mass (after electroweak symmetry breaking). The photon is massless.
The Higgs boson decays to photons via a charged, massive intermediate particle (dominantly a top quark or a $W$-boson). A charged, massive particle can interact with the photon and the Higgs, and thus provide an indirect interaction between the two.
Elementary particles, such as the Higgs boson and the photon, are not composed of "building blocks." I suspect this has lead you to wonder how a Higgs boson can become a pair of photons. Even elementary particles can change into other sets of elementary particles, so long as special quantities such as energy and charge are conserved. This doesn't mean that the photon and the Higgs have an internal structure, that is, that they are made of "building blocks."