I don't think I've heard of a steel inquisitor who ran out of metals. Can they? Or is there something about their spikes that prevents that?
As I believe an Inquisitor's spikes aren't necessarily well explained up to the third book, I will put the following part in spoiler tags. Feel free to skip it if you want, as the rest of my answer can still make sense to you even so.
An Inquisitor's spikes are hemalurgic tools designed to steal an allomancer's power and grant them to someone else. The process is deadly for the giver and some power is lost overall, but it allows the transfer of powers to even non-allomancers. This also works for feruchemy, explaining the Inquisitor's incredible healing/regeneration abilities.
In essence, spikes are only used to augment Inquisitors, not to give them otherwise impossible powers like metalless allomancy. It simply isn't the way the spikes work (keep reading the books or refer to the spoilers, but I have warned you!). As such, they'll eventually run out of metals if they keep on burning them, just like normal allomancers.
However, you have to remember that the Steel Inquisitors work for the Lord Ruler, the single richest person in the whole of Scadrial due to his monopoly on atium. Also, most cities of the Central Dominance are built near mines and, as such, the Lord Ruler has access to near infinite stores of allomantic metals.
Although Steel Inquisitors might not have access to infinite powers, it is probably safe to assume they have access to near-infinite resources. When they start their "shift", they probably ingest amounts of metals that would otherwise seriously damage normal allomancers (remember that the Inquisitors have increased healing and regenerative powers), which could explain why they never seem to run out of allomantic metals.
Yes, they run out. This is based on how the spikes work, which is a plot point. Relevantly:
Hemalurgy is of Ruin, so it cannot be used to create more of something - that power is Preservation's domain.
It's very likely that they get increased utility out of their metals, as Kandra do from their "Blessings". However, Steel Inquisitors are known to sleep for long periods of time, so their powers seem disproportionally taxing - presumably in metal as well as personal energy. They do have access to a lot of metal, though, working for the Lord Ruler.
The only "infinite" anything is a Twinborn, an Allomancer and a Feruchemist such as the Gold/Gold enemy in Alloy of Law, who can burn metals to compound the effects of feruchemcially storing traits.
It's already well explained before, but I'd like to add something: if an Inquisitor were to run out of metals, he could probably try burning one of his spikes, since they're in connection to his blood stream. Or can you only burn metals that are in your stomach? However, I am not sure this would work, but it's certainly interesting to consider, I think.
yes and no.
as the above answers explain they seemingly do need metals for allomancy, though i would like to add a stronger source from book 3 (HUGE spoiler)
when spook gained the ability to burn pewter through Hemalurgy, he needed pewter to do so
and therefore they can run out of metal, however there are other powers granted by Hemalurgy (spikes)
like the "blessings" of kandra or koloss
that arent allomantic or feruchemistic, and are permanent (as long as the spikes are still there).
although it is unclear where the power was drained from