If a person does Wudu and washes his hands, then rinses his mouth and nose, and washes his face, then he washes his arms from the wrists to the elbows, his Wudu is not valid according to most of the scholars.

It is not obligatory to wash the mouth after eating or drinking, whether you want to pray or read the Quran. But it is recommended for you to do that especially if what he ate or drank was at all greasy.

There is no Shar`i basis for reciting Surat Al-Qadr after Wudu and there is nothing in the Sunnah of the Prophet to suggest this.