Does supplication in the last third of the night have a special answer that is not found at other times, and does the statement (Is there any supplicant that I may answer his supplication?) mean that whatever a servant asks of Allah, He will give it to him?

Supplication in the latter part of the night is likely to be answered, especially during prostration, due to the Hadith in Sahih Muslim: "Our Lord descends every night to the lowest heaven when only the last third of the night remains, saying: 'Who will supplicate Me that I may answer him?'" And due to the Prophet's (peace be upon him) saying: "The closest a servant is to his Lord is while he is prostrating, so increase your supplication therein, for it is most likely to be answered."