Does the verse, "And follow the best of what has been sent down to you from your Lord" and the verse, "Those who listen to what is said and follow the best of it," mean that "what has been sent down to you from your Lord" refers to the Qur’an, and is there good and bad in the Qur’an?

The entire Holy Quran is good. The meaning of the two verses: "And follow the best of what has been sent down to you from your Lord" and "Those who listen to the Word and follow the best of it," is to obey the commands and avoid the prohibitions contained therein. It also means that they should follow what is best in their actions and conduct, such as forgiveness and patience. The preference here relates to following and deeds, and not to some parts of the Quran being better than others.