Jean says car on a un pronounced the Parisian way /kaʁ ɔ̃naɛ̃/. There is no extra phoneme between a and un.

Distinguishing nasal vowels from regular ones is a difficult task for people not using them in their native language.

No sound issue around 7:15. Jean just didn’t make that optional liaison. Note that there is no requirement for consistency with liaisons.

FWIW as a French speaker I clearly hear "a" and "un" in that sentence even if they melt together. Which isn’t to say your observation of the sounds is wrong, just that the French-speaking brain knows to parse that sound sequence as those two vowels. I certainly don’t hear any other sound between them.

As @jlliagre says, he doesn’t make the liaison at 7:15 and it’s not a mistake. Maybe it helps to notice the context: the "c’est" is quite long, suggesting he’s using it a bit like "umm" to give his brain time to construct the rest of the sentence. This could be a reason why he didn’t do the liaison here, as might have been more natural if the "c’est" and following "un" had been generated by the brain at the same time.