Yes, it's Uriel.

Indeed, I do believe it is our Demon Like Judge of Fire. Just in a slightly more portable form.

For those who don't know: Biyu is a direct lingual of the Chinese word 比喻, which means METAPHOR, as the translator has written note. It has two meanings:
1. A figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable.
2. A representative or symbol of something else.

Its a great foreshadow that Biyu will be a symbol of things to come but have no direct nor derelict influence to it.

Her:

But from an alternative timeline where she is older and went on adventures with the novel's Mr. Main Character.

You remember our girl the our MC became the sponsor for, the one that could control beasts? Shin Yoosung, the soul he put in the egg is an alt timeline version of her from the 41st try that became a disaster. Couldn't truly save her, so he went the another path of like reincarnating her. That's why he went to the underworld, to get her soul so he could save her another way

Remember little girl that can talk to animal and tame them using her "tamer of the beast" skill? Her alternate version(specifically she's from YJH 41st run) became one of 4 disaster that will destroy the world. Kim dokja defeated it(because of scenarios) but promised to give her new hope. So KDJ went to underworld, made a deal with the hot Donny mommy to give her soul back. He then bought the dokkaebi egg, and put her soul into it so she can reincarnate, trying to fulfill his promise to give her new hope by giving her new life. Hope this helps