1.a. He needed a wife to manage the estate because he's stupid and to show other nobles he's technically married
2. He probably used the wealth his house used to have but he became a broke bitch because of his mistress
3. This stupid guy was probably the only one she could get her claws on to guarantee marriage because he's a dumbass. Every other guy probably weren't stupid enough or she got chased out by their wives
To answer 3's question. It was said in the story she is only staying around because she wanted our fl to be broken and in utter despair. She only wants to get that position so she can climb higher and make all the nobles who have looked down on her because of her background. But because our fl is positive and doesn't give up, it has made the mistress more pissed off. Pretty much the mistress doesn't want to lose to her because she's (in her eyes) not even that beautiful yet she is and can make any man she wants to bend to her will. But since the fl's husband still hasn't divorced her that to also is pissing her off, cause normally any man would do anything to keep her, yet he still hasn't done it for her. Also sorry if my explanation is incoherent, I am high as fuck.

None of this makes sense.
1) He said he married her for his family reputation, but if he's going to bring his lover to all the social events, what's the point??
2) he paid off her debts to get her to marry him... But now he's also in debt??? Bruh??
3) this courtesan is supposedly super famous and could get any guy. Why is she hanging around this broke bitch? Does she actually like him for some reason? Why did she let him marry a random girl if she wanna gonna get jealous and try to chase her away?
4) how old is the prime minister? Cuz that FML is 16 and he's getting blushy around her. I'm guessing he's like mid to late 20s, so I'm kinda getting the ick.