He's a Lancer because of the telescope! It's sort of odd, but it's magnification ability means it's valid in melee. If necessary I can switch him to a Berserker because he was considered a madman by some at the time. Could be interesting.

Innovation of Understanding is more like... "Ah yes the energy is used like this. I see, it's simple thermodynamics!"

...Sorry, I am hardly a man of actual science. But remember that mystery equals power for Servants and magecraft in general. He couldn't find out true names, or learn what the skill can do without seeing it in action, but as he observes how the ability works more and more he basically deconstructs it down to a science. When magecraft becomes understood by humanity, it weakens greatly. I figured you wouldn't want it to be permanent based on how you reacted to that NP-cutting sword earlier, so I had it mostly stick to fights against Lancer himself with some residual weakening afterwards. Consider that mundane weapons can't really affect Servants and you'll probably get why turning mystery into science would be useful. Going that far would likely require a long fight with Lancer personally involved, though, and he can't really make an NP release ineffective unless he sees it used 2 or 3 times first.

Galileo's Natural Genius is mostly sticking to the mundane. Martial arts, military tactics, sewing, etc., as well as various fields of science. He likely couldn't get Mind's Eye but he could probably get swordsmanship or what have you. If you need a real list, I will make it and check with you if everything else about him is accepted.