A Plaque for Mayberry - S1-E25
Visible crew/equipment: While everyone's waiting for Otis to arrive at the plaque presentation in Mayor Pike's office, after Andy admits to the mayor that he asked the real Otis to show up, it cuts to the mayor walking behind his desk, and we can see the chalk T-mark on the floor where Mrs. Bixby stands.
A Plaque for Mayberry - S1-E25
Visible crew/equipment: When Andy and Barney walk into Mayor Pike's office, they stand beside the two women from the Historical Society, and the faint chalk curved marks are visible on the floor where they stand.
Visible crew/equipment: After Ellie and Andy are turned away by Flint, when they walk back into the courthouse while Barney's lifting the chair, the chalk T-mark is visible on the floor.
Visible crew/equipment: At the Scobey house, after Ben sits in the unstable chair and it breaks, when Andy and the Scobeys rush over to him we can see the two curved chalk actor's marks on the floor, where Ben had been standing moments before.
Visible crew/equipment: When Barney and Floyd are spying on Sam while he's getting groceries, we can see both of the grocery store's windows and its clear glass, but when Sam drives off the left display window has been covered with a matte dulling spray resulting in an uneven matte surface, to prevent the camera and crew's reflections.
Visible crew/equipment: While waiting for Barney to show up at the surprise party, Opie looks out the window and spots Barney, then when Aunt Bee and Thelma Lou take their places we can see both actors' marks on the floor - the chalk T-mark and the curved chalk mark.
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.