Visible crew/equipment: When Richard walks into the dining room with the treat for the masses and serves Rory this special dish, we can see the boom mic 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 reflections of the camera and a crew member are visible on 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.