(1) I don't think you can use a nuclear explosion to propel yourself in space. At least, not very well. I have to give it some more thought, but my understanding is that the force from any big explosion comes from the pressure waves that it gives off. Pressure waves kind of need a medium (e.g. an atmosphere) to propagate through. You'd get some kick from the initial vaporization of the bomb body, but not as much as in an atmosphere. My understanding is the "nuclear drives" use a nuclear reactor to generate electricity or thermal energy, and then use that energy to drive a thrust medium (plasma (i.e. ionized gas) or whatever) backwards. I guess you could also use the energy to electrolyze water, then burn it to get high pressure combustion products, and vent that as its drive system. But it's not clear to me how a pure nuclear drive system would work.
(2) I am in the very very small minority of people who actually liked the original '70's BSG (Bridges as Captain Cain of the Pegasus kicked ass! Easily as cool as Tolwyn!), and strongly disliked the new BSG (at least, the kickoff miniseries. I have never watched the actual show).