This document from CAISO defines it thus:
"Spinning Reserve is the on-line reserve capacity that is synchronized to the grid system and ready to meet electric demand within
10 minutes of a dispatch instruction by the ISO."
Meanwhile UK national grid seem to have phased out the term in favour of "fast reserve", which allows them to count instant non-spinning things like batteries and various demand-shedding mechanisms.
I believe it's distinct from the inherent frequency response of generators. The spinning shaft and running gear of a generator contains quite a lot of angular momentum; brief (sub-second) increases in load draw from this. But the definition of "spinning reserve" above implies that it's not currently generating; it's running at full speed, but the generator terminals are open-circuit. It can then be brought online by manual command. This implies an efficiency of zero for spinning reserve, as it's spinning but not generating.
So to the bullet points:
- To increase torque/power, does more fuel need to be burned (or steam produced) at the instant when more torque is demanded?
Sort of: the system has considerable thermal mass and steam pressure volume, so in the very short term the operator can just open a valve a bit to gain a few percent more torque until the overall pressure drops and the system re-equilibriates. I suspect in practice you need to put more fuel in before you want to achieve a sustained increase in power output.
- If so, does this mean that such generators spend most of their time in a less efficient operating state than they are capable of?
By my understanding "spinning reserve" means "not actually supplying power at all". But yes, necessarily there are some generators in the system which are working below peak output and therefore below peak efficiency.
Or, is the increased torque output simply a transient response?
What is the timescale of this response?
Is there a portion of response (sub-second, I presume) that is simply due to mechanics of the generator, prior to an increase in fuel consumption?
I believe the explanation of shaft inertia covers sub-second output variation. Longer term control appears to be manual.
- How do coal or nuclear plants supply spinning reserve (as opposed to natural gas or hydropower), since their thermal cycles operate on longer timescales?
I believe tomnexus's answer about bypass covers this: the steam is generated and discarded. Reducing the bypass can give "immediate" response, probably over the course of a few seconds.
(Disappointingly, I can't seem to find power plant operations manuals on the internet!)