Concerning the second part of your question, once you got a quantity per decay and, as you recalled, you know the source activity in decays per second, it’s straightforward to conclude that the multiplication of the two gives your quantity rate (i.e. quantity per second, e.g. pSv/s for dose equivalent, which I let you transform in uSv/h).
Note that the absorbed dose unit cannot be GeV, rather GeV/g.
As for radioactive neutron sources, these are not automatically available in FLUKA. You have to start the respective simulation directly from the expected neutron spectrum, which can be implemented through the source.f user routine. For your convenience, a dedicated package that can be fully configured via your input spectrum file has been made available.