I believe that the most widely accepted version of events is that Inquisitors use Allomancy, (Proven in the Hero of Ages Prologue) and that their Allomancy is either just naturally very potent (Perhaps because they consumed the metal at the end of Well of Ascension.) or that using Hemalurgy somehow has the power to enhance Allomancy.
The spikes are also definitely something to do with an Inquisitor's Hemalurgy, and most believe that a piercing of any kind can be used Hemalurgically, if the right conditions are met. As for the spikes, the two eye spikes are indeed made of steel, and the one in the heart is made of brass. (Zane also had a spike through his heart, but I don't know what it was made out of. I'd assume it was made of brass as well, but the book never says . . . ) Then the spike in the spine is made of steel, (as per the end of The Final Empire.) so the unknown spikes in an inquisitor are down to seven.
As for myself, I'd believe that the spike setup is two steel spikes through the eyes, one steel spike in the spine, and one of each of the basic Allomantic metals for the chest. The next question I have though, is why separating the top spikes from the bottom spikes kills an Inquisitor. We know from Zane that one can survive with just one spike through the heart, and I'm inclined to believe that the Inquisitor on the receiving end of the Hemalurgic ritual in the prologue of Hero of Ages had eye spikes, if just because of the wording. What is so important about that final spike?
Oh, and as a side note, I'm pretty sure Zane shows us it's possible to use Hemalurgy without knowing it, but that could just be because he's a little addled.