God said be fruitful and prosperous, and I assume the legal system would be used to aid that goal.
Why would the legal system be used to aid the goal of people fulfilling a commandment from God? Except perhaps in some kind of totalitarian state based on a religious fundamentalist ideology. I don’t know where you are from, but that is never going to happen in the United States, EU, Commonwealth, etc. Possibly the Taliban or Islamic State have looked into these possibilities.
You can force people to get children, through side pressures that are unethical yet not so morally deranged that the United Nations does not get involved.
I don’t know about the United Nations getting involved, but I imagine that most of the suggestions that you make would be overruled by the US Supreme Court, European Court of Human Rights, or other relevant supreme judicial authority in the various jurisdictions.
I don’t think the government can impose an additional tax on childless people. This would be discriminatory against both people who do not have children out of choice and people who cannot have children. On the other hand, many (perhaps most) jurisdictions do offer benefits and/or tax incentives to people who have children. There is a difference between the government offering financial help to people who have to bear the costs involved in bringing up children and the government punishing people for not having children. Also, at what point would the financial penalties begin and end? By what age would the tax system start punishing people for not having children? Would single people be punished or only couples?
Propaganda and a government dating app aren’t totally ridiculous. Denmark has had an advertising campaign encouraging people to have babies, although it wasn’t sponsored by the government. How acceptable it would be would depend upon the tone and content of the advertising. I don’t think the government could guilt trip people into having babies, but it could send out positive and encouraging messages about how having babies is a good thing. Dating apps are probably something the private sector does better than the government could do. People choose the dating app that suits them best. Putting all those people on one government-owned dating app sounds impractical.
Forcing single people to live as far as possible from resources? That sounds like a terrible idea and one that would surely be illegal almost anywhere in the world. Maybe the North Koreans have tried it, I don’t know. People are single for all kinds of reasons. In Britain we had a whole generation of women who were single because their fiancés were killed in the First World War. Perhaps they didn’t suffer enough and ought to have been further punished by being forced to live in special singles zones. At what age would people be made to live in the singles zone? Would you be allowed a certain number of years in which to get married? Or would you be put in the singles zone at 18 and only allowed to leave when you got married?
Most of these ideas are barbaric and illegal.