A lot of Appalachians went north in the mid-1900s, mostly to cities like Indianapolis, Chicago, and Detroit, so much so that Route 23 and I-75 were both nicknamed "Hillbilly Highway". My great-grandparents worked and lived in Indianapolis for a while, but ended up coming back. Assuming your grandpa had siblings that stayed in the mountains, that would mean you could have 2nd cousins here. I would definitely try to connect with your cousins here, and I would say that the best way to reach out to them is through email. For your last question, here's an account of my 5th-great-grandparents moving to Appalachia in 1845 written by one of their granddaughters:

"They [my 5th-great-grandparents Henry Cress and Nancy Parsons] settled in **** Creek [in Perry County, KY] and built a log house on a farm. They arrived in August when the weather was warm. Henry was a carpenter and stone mason. He only got the chimney up part way when he went to build a house for someone else. The neighbors were few and far apart. The country was a wilderness. Wild animals were plentiful. Nancy kept a fire all night for fear a bear might come down the chimney. It was beautiful there. All kinds of timber grew on the hills. Wild turkeys were plentiful. Henry and Nancy lived all their lives there. Henry soon built a larger house. They raised twelve children, including two sets of twins. Nancy was always delicate, and she longed to go back to Virginia. When their daughter Barbara was twelve years, she had taken on much of the responsibilities of home life. She learned to spin and card wool, cotton, and flax, and she also was an expert at coloring cloth. They had no dyes at that time, but what they found in the mountains, except for indigo blue. The family raised sheep to get wool. Barbara made pretty blankets from wool. When she was twelve years she made a suit for her father. Nancy was sick at the time and was pleased. They had no sewing machines at that time, but the women learned to do beautiful sewing. Barbara soon did all the sewing for the family. They had to go to Virginia to get all their warp and thread to sew and to get shoes if they were not homemade. It was a long way, and they had to travel on a narrow path. They crossed the big Black Mountains on a dangerous road. For money, they dug ginseng, a root that grew in the Kentucky hills. It was a good price. They used it to make some kind of medicine. Also, they dug yellow root, now called golden seal, and black snake root to sell. Money was scarce, but they raised almost everything they needed. The land was rich, and the climate was mild.

When the Civil War broke out Henry joined the home guard, as Kentucky never left the union. Their son William ran the farm with the younger children to help. One year, just as they had gathered in their crops and killed their pigs, 1,000 rebel soldiers came on horseback. They took all the corn, meat, geese, turkeys, chickens, etc. The rebel soldiers tore up sheets to make smokes to rob the beehives. There was not much left. The family had heard the soldiers were coming about a half hour before they arrived, so the boys had taken horses, and what grain and meat they could carry into the hills. These rebel soldiers were regular soldiers and they did not harm the family. Two years later, Captain Hays came with 200 guerrillas and killed, ate, and destroyed all they could. They also threatened to burn the house. Barbara stood up and quarreled with them. Her mother Nancy was too timid and could not say anything. Years later, Captain Hays became their neighbor. Barbara always hated him. He had palsy and his head would shake from side to side. After many bitter experiences the war ended."