If you’re talking about the published FR charts (specs), then along with most of the other specs, they have been measured at the amp’s optimal/nominal output level or at a prescribed (standardised) level which is also almost certainly at or very near the amp‘s optimal output level, because obviously the manufacturer wants the specs to look good in comparison with other amps. Typically that nominal/optimal level would be around a 50% output setting, EG. A 40% - 70% setting, although it can be a wider range in some amps. In extremely few cases (if any) would a 100% output level still be optimal, so THD, IMD and noise are all likely to be significantly (and audibly) higher at 100% output, as well as some other factors (such as crosstalk) and the FR and other measurements at 100% are very unlikely to match the published charts/specs.
For the reasons above, although there’s no real way of knowing what that “headroom” is. For example an amp manufacturer may have it’s max output setting be lower than it’s actual max setting, thereby providing it’s own “headroom” even at a max setting and in some cases amps have built-in protection, although that’s also a function of the input level.
It’s relative. In all or virtually all cases, a 50% setting would add less noise than a 100% setting, however a very low output setting can raise the noise floor, so a 50% setting may result in less relative noise than say a 10% setting. However, this latter scenario is very dependent on the design of the amp, even a setting lower than 10% might result in less noise than a 50% setting in some/many cases. Theoretically of course, the lowest noise would be achieved with no gain.
G