Yes, laurel killed one of our sheep.
I would say it's very un-neighbourly to plant so close to the fence. Two - 3 feet away would be reasonable. Depending on the species of bamboo, it could soon invade your plot, and the hazel will definitely hang over the fence.
I love hazel, which would provide you with nuts, but what a shame he's not taking this opportunity to grow a mixed native hedge for wildlife as well as screening.
One upside of the hedges/screen, is that they will provide you with a bit of biosecurity. He will need to double fence the hedge, so his own animals don't demolish the hedge before it's grown, and this will prevent nose-to-nose contact between your livestock and his - all without you having to do a thing.
I believe he can plant whatever he wants, but a friendly discussion about the laurel and bamboo is in order. Perhaps he doesn't know that laurel is poisonous.
One plant which can be grown as a hedge, is pretty, cheap and impenetrable, plus not poisonous to stock, is Rosa Rugosa. It flowers in summer and provides huge hips in autumn for wild birds and poultry. Maybe suggest that to him.