Will fix the name issues, thanks
Skill base refers to a weapon skill's base stat buffer. For example, a light weapon with "light assault" means the skill base is S (small), "shining" referring to M (medium) and "luminous" L (large). Alternatively, you can link the rarity of the weapon to the skill base (R weapons only have S skills for example), but the trap is that due to dual skills being a thing, an SSR weapon won't always have an L skill, it may have dual M skills.
The team builder HP is the party character page. The character specific screen isn't necessary as the base HP is pretty much the same for all himes, using stats from the party screen can account for eidolon, weapon and accessory stat mods.