I'm going to give the sword repair a "Pass" because it could be written off as mithril/magical metal bullshit, but if that was a steel sword... No bueno. Doesn't work that way. The blade would be incredibly fragile. Reforging it would be the only option. But, again, it's mithril, so maybe there's magic super material shit at work. (That said, even Eizo eventually resorted to reforging it, but for magical reasons instead of metallurgical.)
Also, borax is not required for "adhesion" - it's used as a flux to prevent oxidation and helps keep impurities out of the material. Otherwise what can happen in the forging process is you can get impurities, scale, layer separation that leads to delamination because you don't actually have a solid piece of steel, etc. And you can still fuck up a forged piece even with borax used as flux on the piece.