NHF – new heroes for Heroes V 3.1.

Will the additional level be provided by a skill amulet or by leveling up? Or are both options relevant?

Neither of those.
1) Currently, the Absolute level can be given either at the start or through scripts (which doesn't prevent scripts from being linked to, for example, the moment the amulet is worn, but why bother?).
2) NHF is not a mod for new skills, but a mod for new hero specialties. As a specialty for a specific hero, it's not bad (Absolute Chaos Magic, for example, has long been available to the Warlock Kaldorin), but as a specialty for everyone, it's a different mod.