Artifacts that provide a percentage bonus to necromancy only work if the hero has the spellcasting skill, and other artifacts that grant a percentage bonus (resistance, eagle eye, archery) and artifacts that reduce the ransom price by a percentage also work on the same principle, meaning they only work with the corresponding skill leveled up?

Not exactly. You need to read the description more carefully. In one case, it says "+% to skill ***", which means it requires the skill itself. In the other case, it simply says "+% to ***". In other words, in the case of Necromancy, Archery, and Eagle Eye, the skill itself is required. In the case of Resistance and Diplomacy, it is not, because it says "increases resistance by x%" or "reduces the cost of surrender," meaning the artifact does not enhance the effect of the skill.