Can someone please tell me what killed me so fast in the first clip?.

First clip in video, rest are testing dmg.

https://www.youtube.com/watch?v=cJuC4uEfNrU

Btw Spoilers for first interlude boss.

Probably an unlucky crit.

I don't remember if GGG changed it for PoE2, but in PoE when an ability rolls a crit, every hit of that instance will crit.

That fire go further than you can see it. Seen people dying to it multiple times while well out of that cone but not far enough.
Not sure if it's what happend to you but it's not uncomon for that boss. Really need to be further away on her back when the fire reach her.
It's not very clear visualy tbh.

So unlucky, rip HC character

Probably an unlucky crit.