Why is Earth's inner core made of an iron-nickel alloy?
The first thing you should think about is how the accretionary disk cooled and the cosmochemical constraints this put on Earth (But I am not going into details here). From studying meteorites it is apparent that the oldest meteorites don't show signs of chemical differentiation (e.g. melting, ...) and are thought to represent the solids that formed from the accretionary disk. Because of their characteristic round structures, chondrules, they are called Chondrites. The most chemically primitive Chondrites (e.g. https://en.wikipedia.org/wiki/Allende_meteorite) roughly have the same composition as Earth. This is why it is thought that Earth formed by accretion of these smaller chondritic objects.

There are also other meteorites called "achondrites", meaning "no chondrules". They show signs of chemical differentiation (we can find stony-, stony-iron-, and iron-achondrites). For this chemical differentiation to happen it is necessary to think of the meteorite as having a parent body, on which this differentiation took place. These parent bodies differentiated similar to earth into an iron-nickel core (iron-achondrites), an olivine-rich mantle (stony and stony-irons) and a silicate crust (stony-achondrites). Because differentiation takes time, it is somewhat unlikely that a parent body formed, was destroyed and the iron-core was recycled to nucleate Earth (Earth has roughly the same radiometric age as many meteorites). So your suggestion C would take quite some explaining. Also suggestion B is not temporally possible, because the magnetic field needs a liquid iron core to work and therefore only came into existence after the iron migrated to the core.



A few words about iron-nickel. This has something to do with the abundance of elements in the accretionary disk (http://upload.wikimedia.org/wikipedia/commons/e/e6/SolarSystemAbundances.png). Iron and Nickel are very common elements. They are also siderophile, which means, that when a chondrite melts, the iron will try to separate from the sulfide- and silicate-melt. Because of the larger density of this melt, it will try to move towards the core of a planet. But it is very likely that other elements form a certain percentage of the core's chemical composition and it can be reckoned that this will be similar to some of the compositions of iron-meteorites.

If you get more interested in this I can fully recommend "McSween, Harry Y. (1999). Meteorites and their parent planets (2. ed. ed.). Cambridge [u.a.]: Cambridge University Press. ISBN 978-0521583039." which is very enjoyable to read and because of its descriptive approach not outdated. The newer book is also very good "Huss, Harry Y. McSween, Jr., Gary R. (2010). Cosmochemistry. Cambridge: Cambridge University Press. ISBN 978-0521878623.".