Is it true that Allah didn't grant the angels the wisdom to read and understand the Quran? Why? Is it the same with the shaytans?
The few opinions I found say that it is a baseless speculation to say whether the angels can or cannot read the Quran since we have no conclusive evidence either way.
As for the jinn (shaytans are considered a type of jinn), the Quran mentions them listening to and understanding the Quran:
29. Recall when We dispatched towards you a number of jinn, to listen to the Quran. When they came in its presence, they said, “Pay attention!” Then, when it was concluded, they rushed to their people, warning them.
30. They said, “O our people, we have heard a Scripture, sent down after Moses, confirming what came before it. It guides to the truth, and to a straight path.
31. O our people! Answer the caller to God, and believe in Him; and He will forgive you your sins, and will save you from a painful punishment.” (Verses 46:20-31)
Sura 72 gives more details.