Visible crew/equipment: When Richard walks into the dining room with the treat for the masses and serves Rory this special dish, the boom mic can be seen bobbing about in the reflection on the window, at the left side of the screen. (00:00:15)
Visible crew/equipment: While Lorelai and Rory are making a list of everything Luke needs to fix, after Lorelai mentions Dick Van Dyke, the camera and a crew member's reflections can be seen in the left glass door of the corner book cabinet. (00:07:55)
Visible crew/equipment: After Lorelai gets off the phone with Richard, when it cuts to the bakery we can see the reflection of the camera as it moves past the chrome display case. (00:11:50)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.