Is it permissible for the wife to waive her deferred dowry for her husband? Is the deferred dowry forfeited upon divorce? And is it permissible for a man to promise a dowry that he does not possess?

There is no harm if the wife forfeits her right to the Mahr (dowry). The deferred Mahr becomes due upon divorce after consummation, unless the Khul' (divorce at the wife's instance, usually by giving consideration) is for that money. It is permissible for the husband to say he will pay such and such as Mahr even if he does not possess it, provided he clarifies that it is deferred and remains a debt owed by him.