When Murdach is in woods surprising Claire - he sings "Boogie Woogie Bugle Boy" That was not recorded till 1941. But he learned the tune in Season 1 when he and Claire were traveling cross-country to find Jamie and she was entertaining small towns with a singing act.
Blue Ridge and Piedmont are two different North Carolina regions. Jamie and Claire were on a journey to the Blue Ridge (Mountains) to find land. However, when Jamie signed the documents the governor called it Piedmont. Piedmont is the central region of North Carolina with very little mountains.