Secondly why trusting Lae'zel is a rational thing to do? She is unclear about what the purification might entail, she's alien to Faerun and the way you meet her after Nautoloid crash shows that she would be unable to survive on her own. For me it's clear that she is joining you because she needs you, not other way around. Furthermore, all other companions suggest finding Halsin as a better bet for cure.
On my first playthrough I didn’t go there until after finding Halsin because purification sounded like they were going to kill the party to me.

She wasn’t very happy at the party.😜