There isn't any unusual accent in that speech. What you're referring to, though, is intonation, and one of the things you're specifically referring to is called vocal fry.
In vocal fry, the vocal folds are shortened and slack so they close together completely and pop back open, with a little jitter, as the air comes through. That popping, jittery effect gives it a characteristic sizzling or frying sound.
Vocal fry has been gaining a lot of attention in the past few years, but it is not a new phenomenon, nor is it limited to women. Listen to Noam Chomsky sometime; he has it as well. One difference is that he has it a lot, and his register isn't all over the place, so it sounds more natural with him. But if you listen carefully, sometimes it's pretty bad. (Or he has vocal nodules. I don't know. Maybe both.)
From Language Log:
The following things about vocal (creak and) fry are clear:
- Everybody does it.
- Everybody has always done it.
- There's a widespread belief that young American women are now doing it more (than young women did in earlier decades, or than older women do now, or that men of any age do it or did it).
- No one has ever presented any non-anecdotal evidence that (3) is true.
(He relents a bit on that last point, however.)
Edited to add (post OP's edit): Again, I don't hear an accent. The speaker is trying - maybe a bit too hard - to speak about a chemical reaction in a not-too-monotonous tone, varying her pitch in a slightly exaggerated manner (at least that's my understanding.) The register is on the formal side - it's a teaching video. Rising question intonation - often called upspeak - is not very prominent on this video (it questionably occurs maybe twice.)
The article cited below goes into some detail about upspeak and vocal fry, as well as the negativity it has attracted.
From Upspeak To Vocal Fry: Are We 'Policing' Young Women's Voices?