This Bible contradiction is from the Skeptic's Annotated Bible.
No, even God has to rest sometimes.
Genesis 2:2-3 View context
And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made.
And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made.
Yes. Jesus and his dad always work on the Sabbath.
John 5:16-17 View context
And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day.
But Jesus answered them, My Father worketh hitherto, and I work.