Hello, I don't know anything about your life or what you may know about God, but I have answered these as best as I can. If you have any more questions, I would like to answer - if I am able.
Could God do evil if he wanted to?
Would it be possible for him to want to do evil?
Learning from God I found that He cannot and will not go outside of Himself. He is Holy and not unholy. He hates sin to the deepest part of the abyss (which is more than any of us humans could possibly understand). That is not to be confused as God hates humanity which He created in His image, that is not so. Other wise, Christ never would have walked this earth to sacrifice Himself for a defense to His name and for many.
Is anything God does by definition good.... but if I were to do it then it would be evil?
What is good? If you mean by the world’s definition then there is nothing good - because it is from the world and not God. God is Good. He is Good because of His Holy nature. What Christ did was Good because He followed His Father all the way to the cross - and even after that. Everything Jesus Christ did was Good in Father God’s sight. Even Jesus Christ Himself denied that He was good and reminded the people that only God is Good. He denied Himself for His Father’s name, an example of denying oneself:
Mark 10:18
Luke 18:19
Being born into the world, we are in a fallen image of mankind because of what happened in Genesis. However, Jesus Christ did make a comment about evil people doing good:
Matthew 7:11
Luke 11:13
The mission of Christ was for people to believe in Him so we can also share the Victory He already won. The Sacrificial Lamb of God, where no blemish was found. Perfect in every way and Jesus Christ continues to be our High Priest on our behalf (those who believe in Him): Hebrews 4:14.
Is there a principle of right and wrong that transcends God?
Anything outside of God is sin. Imagine creating a world that is your own and creating everything in it. Would the one that is the creator give up or surrender one’s right of absolute Truth?
God is Truth and Love. Everything He has created is by His design. Naturally, He should get all the credit - even by the breath we draw did He give His life for all.
I know no one as loving as this One.
I hope this was helpful to you.