the amount of times I googled 'taxis' with predictable results

Yeh I don't think the plan is to chain the reaction, just have a high energy neutron generator driving the reaction

I'm not sure about the cost, but I remember that for some medical aplication there are some protons rays to neutron rays "converters". (IIRC it's a target of berilium that absorbs the proton, splits, and release a neutron. IIRC) They are easy to turn off inmediately. (IIRC)

Yeh.