Meaning of "But you are faking it" and "Rule number one of modern life"

Question

Vicki said, ‘Don’t you care about Philip and Athena?’ said Vicki.

Elizabeth said, ‘Course I care. I always care. But there’s no point in making a song and dance about it, like that night he stayed here. Know something? There’s only one thing that’ll bring ’em back, and that’s indifference. The one thing you can’t fake.’

‘But you are faking it.’

‘At the moment I might be. But as soon as it stops being faked and starts being real, he’ll turn up. Rule number one of modern life.’

Vicki shuddered. ‘You’re cold. You’re too detached. You’re scary’

explain: "Elizabeth is philip's lover and now philip and Athena have travelled with each other"

1. Does "Your are faking it" mean "you are faking that Athena and philip are in love with each other" or "you are faking that you are in love with philip"?

2. Does "Rule number one of modern life" refer to "he" and mean: "he will Rule number one of modern life" or does it something general and mean "you should rule number one of modern life"? its meaning is unclear to me.

And dose in this context "detached" mean "unemotional"?

Source: The children's Bach by Helen Garner.

Answer 1

1. The previous statement said that indifference is the one thing that can't be faked. So I interpret "But you are faking it" to mean "But you are faking indifference" (i.e., you're not actually indifferent, you're only trying to look like you are).
2. "Rule" is not a verb here, it's a noun. It's like saying "That is the number one rule of modern life." They're making a general statement about modern life, that the most important principle is what they just mentioned - that when someone is truly indifferent (not just faking indifference), the other person will turn up.
3. Yes, the meaning here is like "unemotional".