Is a photon able to transfer an impulse to a neutron or, and this is the same, can light accelerate a neutron?
Yes, a sufficiently energetic photon can accelerate a lone neutron. The kinetic energy imparted to the neutron reduces the photon's wavelength (redshifts it) by the same amount, so the total energy of the system remains the same. Outside the nucleus, the neutron has a half-life of about 10.5 minutes.
Neutron has electric and magnetic polarizability (https://en.wikipedia.org/wiki/Neutron), so light can polarize neutron, which in turn will emmit light as a result of being polarized. The net process will be light scattering of the neutron. Since light can carry momentum it is probably possible to conceive of experimental setup where momentum carried by light will be passed onto neutron as a result of light scattering.
Yes, when a photon reflects of of a reflective surface, it can accelerate that surface. This is used in solar sails. Now, since a surface contains neutrons, a photon can accelerate a neutron.
Sadly, this way of accelerating a neutron is rather indirect since the photon really just accelerates the surface which contains neutrons.
If you wanted to know whether a photon could directly accelerate a single neutron, than I am afraid that I cannot provide an answer.