Is it obligatory to make up prayers that were performed with previous ghusl and wudu, and are the actions taken to deal with the whisperings during prayer—such as going with the first thought regarding the number of rak'ahs, and considering the act of recitation and glorification as completed without prostrating for forgetfulness—correct?

The original ruling is that previous prayers are valid, because doubt about an act of worship after completing it has no effect. Therefore, there is no need for a make-up prayer. The remedy for obsessive whispers (waswas) is to disregard and ignore them, to base one's actions on what is most certain, and to assume that the action has occurred when in doubt about it.