Neutrino annihilation and bosons

The neutrino and the anti-neutrino can annihilate to create a $Z$ boson. But the mass of the $Z$ boson is around $90$ GeV, so in order to create such a boson, the neutrinos need to be high energetic.

Theoretically, a Higgs boson could be created as well, but for that an even larger amount of energy is needed, since the Higgs boson is heavier than the $Z$ boson. Moreover, the coupling of the Higgs to the neutrinos is extremely small. The Higgs boson's coupling is proportional to the mass of the neutrinos. Neutrinos are known to have a non-vanishing mass but a very small one. Because of the very low mass, the coupling is also very small. This is not a process that likely is going to be observed in an experiment.

On the other hand, the creation of photons is not possible at all. Photons couple to electric charge. Neutrinos are neutral, hence no coupling to photons.

Maybe even more interesting than a neutrino-antineutrino annihilation would be the observation of a neutrino-neutrino annihilation. If neutrinos are their own antiparticles, we call them Majorana neutrinos (otherwise they are called Dirac neutrinos).

We don't know if neutrinos are Majorana or Dirac. If we would observe a neutrino-neutrino annihilation, it would be a clear sign that neutrinos are Majorana. But neutrino experiments are notoriously difficult to carry out. The only experiment that I know of that is looking for a neutrino-neutrino annihilation, is the neutrinoless double $\beta$ decay.

Yes, the Z boson can decay into a neutrino and anti-neutrino, and the process you describe is just the time reverse of this.

But also we have to note that photon pair creation through neutrino anti-neutrino annihilation is possible at higher orders in perturbation theory (starting at the one-loop level with the exchange of charged leptons and $W^\pm$ vector boson). This process has indeed very small cross section because of the loop integral suppression factor.