Is it some sort of pre-God Ki that is going to eventually transcend him to the level of a God? And how was he able to even remotely fight black after Goku and his dad were already defeated?
There is no official explanation, but manga #24 has given a very important hint that can possibly be the answer (spoiler)
Trunks is officially a kaioshin apprentice, he can use kibito technique to heal other people, and since kaioshins have god ki, as kaioshin apprentice he probably has some grade of knowledge on god ki.
There is no official explanation. Even in the show none of the characters seem to care enough to question it. I like to call it SS demigod blue because that sounds cool. I'd say he just started to adapt blue god ki after feeling it from his dad and Goku. As for why this lets him fight evenly it's probably just cause there isn't going to be another arc involving him. He deserved to have this moment and the author just gave it to him.
When goku fought Beerus, Beerus said goku's body learned from the experience the power was now his and later goku revealed that vegeta learned to harness god ki without the ritual I believe with the saiyans ability to grow stronger after each battle that's how this was possible but with trunks being half human he won't be able to fully harness saiyans god ki fully but he learned from the experience of fighting a diety and was able to somewhat harness it or if he can fully use saiyan god ki this is the form in between regular super saiyan and the god forms because he is still learning to use god ki that's what I believe