When Tessia get's her body back, was her core reformed or did she form a new one? Tessia having integration and a white mana core makes more sense, but it implies too much.

Wouldn't Tessia reaching integration twice possibly kill her, or would she have to become stronger to integrate twice? Would her body allow her to integrate twice? If she can't integrate twice due to being a lesser, could she have two beast wills? Lastly, since mana core's aren't just made of mana, and when a core is shattered, it stays in the body, if Tessia's core cracked or shattered, would it be integrated or be repaired?