Does a divorced woman's right to deferred dower (mahr), maintenance during the waiting period (iddah), and compensatory gift (mut'ah) fall if she does not claim them? And are these considered by Allah?

If the divorce is based on ibra' (absolution/release), then whatever was agreed upon to be relinquished, such as the deferred mahr (dowry), is forfeited. However, if ibra' was not stipulated, then the wife retains the rights of a divorced woman and may demand them judicially, or she may forgo them and seek her reward from Allah.