As you read through this I'm sure you thought at least once what Vexalia is and how she works, so I'll leave this here to explain exactly how she works.
Speicies: Vexalia doesn't belong to any specific species, as previously stated in the story, she was created using Vexus' remains, but since they weren't exactly complete, there were fillers as well, these include pieces of Hylia herself along with certain carnivorous animals, meaning Vexalia isn't really anything, if not an amalgamate.
Powers: At the start Vexalias powers were all bio-punk based, this is because the process of her creation was incredibly slow, so when she was found by Gaepora in the prologue, she actually wasn't complete.
Now since Vexus was technically a piece of the Harbringer of Demise, Vexalia also resulted a little corrupted, causing everything that should have been a holy power of some kind to be turned into a grotesque and fleshy parody of what they were, however this was fixed as gathering the three sacred flames purged the corruption bound to Vexalia allowing her to be complteted.
Boiling Blood: Anything that was caused by Vexalias blood overheating was completely caused by the influence of the Harbringer, forcing her body to adapt to the absolute extremes and doing stuff that severely damaged her.
With the influence gone however, the boiling blood state was kept, but it's effects are ever so slightly different, which will be seen the next time it is used in the story. (Chapter 43)
The Master Sword: Not really called that in this story, but the new name shall be revealed in the next chapter, anyhow, the Master Sword was also very incomplete when Vexalia found out, but not as in the canon Skyward Sword where it began as the Goddess Sword, here it didn't even have a physical form, only the aura was present in the pedestal if you remember, and once Vexalia made contact with said aura, her body formed a sword to house it.
And that was it everyone, unless you read the one below, but I don't advise it, do if you want, but you might regret it, either way I hope this cleared up some things as to how Vexalia functions.
Extra Information (THIS CONTAINS EXTREME SPOILERS, READ AT YOUR RISK): Vexalia has a power born from the mixture of Hylias and Vexus influence within her, she was never meant to have it, and there is no way for her to access it, no knows its there, but it can be forced out if Vexalia were to somehow manage to go beyond exhaustion and push through her own life, but the consequences would destroy absolutely everything.