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.

If you have a wound and you want to make Wudu, there is nothing wrong with you leaving the bandage on; rather you have to leave it on because it is in your interests. You can wipe over the outside of it when you wash the part of your hand that is not covered.