The fee could be to the government (and this is the way I interpreted Shankar's comment), so a kind of tax on applications. This seems to resolve the issues you mention except for the first one. For that a small monthly subsidy based on some function of income/having a job or not/wealth could be an idea.
Then a similar thing could be done for job openings by companies to avoid fake job listings etc.?
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The fee could be to the government (and this is the way I interpreted Shankar's comment), so a kind of tax on applications. This seems to resolve the issues you mention except for the first one. For that a small monthly subsidy based on some function of income/having a job or not/wealth could be an idea.
Then a similar thing could be done for job openings by companies to avoid fake job listings etc.?