Who said anything about infinite? I don't see anything wrong with importing labor if it's of net benefit to our society. If there was genuinely no citizen that wanted the job for any reasonable price then what's the harm in bringing in an educated outsider who contributes positively? It improves several metrics simultaneously without harming anyone.
You could also say that India is below replacement fertility. Which, if Indian history is anything to go by, will mean India will outlaw emigration to protect ultra-rich Indians.
China has already mostly made emigration illegal. The rest of the world will follow.
Depends what you mean. Communism loves bureaucracy and so there are 10 different system "totally not cooperating" to prevent leaving. In China you need permission to leave the country (or even your town), and so there is no law change. The big bureaucracies are referred to as "Hokou" (within China) and "Exit-entry administration" for international. So no direct announcement, everything is under direct control of Xi. You see, it was always illegal to go outside of the country without Xi's approval and those approvals have mostly stopped coming.