Positron-electron annihilation - can more than two photons be created?

Yes, the requirement for at least two photons is because a single photon would violate conservation of momentum. See my answer to Particle anti-particle annihilation and photon production for a (very simple!) proof of this.

Annihilation can produce more than two photons. In fact the decay of ortho-positronium to two photons is forbidden, and it (mostly) decays into three photons. This is a bit of a special case though as it's due to conservation of angular momentum in a bound state.

The LEP accelerator and the experiments running on it were e+e- annihilations, the energies on the Z resonance and also up to 210GeV . These annihilations had a large variation in the particles detected and a great number of decay channels published in numerous papers.