Visible crew/equipment: After Barney tells Andy that the stranger may be a foreign spy Ed Sawyer walks into the courthouse, and behind him a crew member's hand can be seen catching the door just as the door closes.
Visible crew/equipment: When Andy walks into the barber shop while Barney's complaining to Floyd about his sideburns, we can see the white T-mark on the floor at the bottom of the screen, as well as chalk marks where Andy's standing.
Visible crew/equipment: At the end, when Andy opens the door to Floyd's so Ed Sawyer can get a haircut, the set's large spotlight is reflected on the door's window.
Visible crew/equipment: While Floyd's napping in the barber chair, Andy's reading the newspaper, and when Barney walks in the actor's two curved chalk marks are visible on the floor, where he will stand.
Visible crew/equipment: While Barney's in the barber chair, Floyd starts talking about how he'd tried living at the back of the barber shop, and when the shot faces Barney we can see the reflection of a crew member's legs moving around - the only ones in the shop are Barney, Floyd, and the two men seated by the corner.
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.