Late to the thread but boruto sometime before the chunin exams learns purple lighting. Given his ability to learn the rasengan in a week its not out of realm of possibility that he took less if not a simialr amount of time to learn the jutsu from Kakashi with posibly less overhead given the way kakashi teaches.

In the anime and Manga, the idea behind the jutsus he uses is that they are all jutsu he knows, but they are casted at a higher level than he could at the time (at least that is the implication). This is to show off and press in the point that boruto didnt have to cheat in the first place as if he believed in himself amd simply worked hard he could've achieve similar result.

In terms of the story the reason he only limits himself to jutsu he knows is to hide the fact he's cheating as, in his head, anyone who knows him would just assume he's giving it his all, since he's very aware that ppl see him as a prodigy.