Natural Born Genius A++ is basically imperial privilege you'll have to list which specific skills he can use. This is for the sake of balancing the character stealing things like mind's eye, and other techniques is a bit of a long shot. 

Innovation of Understanding A seems more like he'd just be able to find out names, or what specific abilities are instead of directly downgrading the skill, or weapon itself. How does it even work when put against legendary weapons like Lancelot's Arondight for example which is a weapon that is divinely made.

Most importantly how does Galileo meet the requirements for the lancer class? I used the word "spear". and "Lance" as search words and didn't find a single thing about polearms in his entire wiki.