Is it permissible for the husband to buy a house for his first wife only and favor her in maintenance, while the second wife spends from her own money, and what the husband allocates for her is insufficient?

It is obligatory for the husband to be just between his wives in terms of expenditure and clothing according to their needs. He is not obligated to be just in anything beyond that. Thus, he may favor whomever he wishes with anything exceeding the obligatory expenditure, clothing, and housing. For example, he may grant ownership of a house to one wife and not the other, as long as he has provided housing for the latter. If one of the wives has more dependents, he is not obliged to equalize her expenditure with that of her co-wives, because the expenditure for dependents is originally obligatory upon the man, and he must give them their sustenance in addition to their mother's sustenance.