Is it permissible for the judge to accept Khul’ without the return of the Mahr, or what should a wife do who desires Khul’ but does not possess the money to return the Mahr, given the husband's refusal to divorce and the wife's inability to provide the money or obtain assistance from her family or friends?

If the husband harms his wife (by not providing maintenance or by causing her harm), she has the right to seek a judicial divorce. If there is no harm but the wife dislikes remaining with him, her only option is Khul' (dissolution of marriage by mutual consent, usually with the wife giving compensation), by returning his Mahr (dowry) or whatever they agree upon, as the wife of Thabit ibn Qays did with the Prophet, peace and blessings be upon him.

The compensation for Khul' may be breastfeeding the child for a specific period, or the husband residing in her house for a specific period, or bearing the responsibility for the child's care or maintenance for a specific period (even if the duration of breastfeeding or the exact amount of maintenance is not specified, customary practice should be referred to), or maintenance for a pregnant woman's pregnancy, or waiving the deferred Mahr. All of these are permissible.

If the woman owns nothing and the husband insists on getting back his Mahr, that is his right, and she must wait until she finds the compensation.