My take, for what it is worth!

As couples do -- Kay left the lamp on so that Michael didn't have to stumble in the dark

Kay was aware Anthony's drawing was on Michael's pillow -- Kay saw Anthony leaving the drawing or saw it after....

Fredo wasn't in, on Michael and Roth's big deal. We have exhausted! Fredo's "a little help": options
Sure thing Fredo had to do something “His only value would have been to open the drapes”