Finally a good plot hole! But these aren't really plot holes as much as errors in reality testing. It's more of a "I found it hard to believe…"

1a) Franck and Elizabeth's "lack of chemistry." Did you miss the scene where Franck drops by suddenly, threatens her, and gets up in her grill? The original deal they make sitting at their own table? Her natural attraction to power (as a prior victim of abuse). Her own hypnotic sexuality and his French badboy suave?
1b)…

I agree that there are implausible lurches in the plot, but I disagree with your second suggestion, "Why the hell did she keep on treating him?" Elizabeth states the answer in plain English. After legal recourse was refuted (agreeably implausible), her only solution to HER PROBLEM is to hypnotize him. She isn't…