Yes Benjamin was alive when his older (full) brother was sold into slavery (Genesis 37). Joseph and Benjamin were the children of Rachel and Jacob. Rachel died giving birth to Benjamin (Genesis 35:16-20).
Benjamin, however, did not take part in selling Joseph into slavery because he was too young to do so.
Genesis 37:28 Then there passed by Midianites merchantmen; and they drew and lifted up Joseph out of the pit, and sold Joseph to the Ishmeelites for twenty pieces of silver: and they brought Joseph into Egypt
The book of Genesis chapter 43 is in the telling of the story of Joseph and his brothers who sold him into slavery. The story starts in chapter 37 and goes through chapter 50.
Joseph (one of the 12 son's of Jacob/Israel) was sold into slavery by his brothers and taken to Egypt. Not really an exile, but he was brought "by chance" there. His family ends up reconnecting with him during a famine; and from there they grow to be over 1 million (estimated, of course.)
Abraham, Isaac, and Jacob were definitely businessmen. So was Potiphar, to whom Joseph was sold.
The key passages that include dreams would be Joseph, who was sold into slavery and became second to Pharaoh in Egypt, and Daniel. Genesis 37:1-11 Joseph has two dreams Genesis 40:5-23 Cupbearer and baker each have a dream Genesis 41:1-7 Pharaoh has two dreams Daniel 2:1-45 Nebuchadnezzar had dreams that Daniel interpreted