Why pair production and annihilation cannot occur in free space?
I’d say it is because pair production requires the presence of a very strong electric field, typically the presence of an atomic nucleus.
Particle-anti particle pair production and annihilation happen constantly even in free space.
Space constantly produces particle-anti particle pairs. They are called virtual particles because they are very short lived and quickly annihilate each other.
Although this appears to violate conservation laws it actually doesn't. The Heisenberg uncertainty principle allow energy to be borrowed for a short period of time. This accounts for the mass of the virtual particles.
An interesting consequence of this is if virtual particles are created near a black hole. If one particle enters the black hole and the other doesn't then the black hole must lose mass to compensate. This is Hawking radiation which can ultimately cause black holes to evaporate.