Let me settle the debate since I made it
1. World of IHS is based around honor society. Meaning that two people agreeing to something without written world is as sacred as in our world written deal with your finger stamp. That also means that people do not throw deals lightly, it isn't like our modern world where everyone is bullshiting all the time and they have zero consequences. Hey bro if you house will burn down you can sleep with me to rest of your life. In our world you would just roll eyes but in honor society this is different, you treat such promises seriously and people who break those promises live in shame.
To the point. Jack and Sylvia were bought as family because they declared themselves as such at the time. They met 2 years ago and they are less than 2 years together. At any point either Jack or Sylvia can come to mistress and declare that they are not family anymore, moreover they are obligated to do that. Not by court but by their own conscience and adherence to honor.
In this case, Fiona tries to bargain with Jack as she can't buy him from Mistress if he doesn't want it and Mistress can't sell him separately because Sylvia and Jack are considered by her as family unit.
2. If they declare they are family then Mistress can't sell them separately. But in this case Fiona wants to convince Jack to come with her but she can't force him nor Mistress can do that. So jack has to agree to be sold separately. It's protection for families.
3. Roleplay aspect. I, you, we know what Jack would do. But someone else might come to different conclusion based on their understanding of characters, choices they made and how he likes characters. Furthermore you got only a choice to make and consequence of that is not in game as whole ending is not finished yet. No doubt such important decision will have impact of characters in the game.
2 reasons:
Mistress doesn't want to get rid of all servants. She's noble after all and isn't used to cook herself, clean etc.
She technically doesn't pay for them. Henry is helping with her finances in major way which means it would be like trying to sell borrowed car from your friend. In mentioned honor society it is a big no no.
The main reason why Mistress agrees to those talks is that Fiona shared with her what she will propose (aside from few ehhhmmm minor details). From point of view of slave those terms were really great, moreover Mistress would receive in return something.
Basically a win-win for Jack and Mistress if you don't count ambience of relationships in the house. Moreover if Jack would leave house it doesn't mean that he needs to break with Sylvia. Obviously they wouldn't meet much if at all but they could still continue their relationship after their debts would be repayed and in Jack's case according to Fiona his case would be much much faster...
