Just some personal experience about decomposition, CPR, and death notifications.
Last August, I went to check on my SIL, whom family members hadn't been able to contact for a couple of days.
I got her key from her neighbor, and opened her front door afraid that I might smell something. No odors. So that was a good sign. However, I found my SIL dead in bed - cold to the touch and with obvious livor mortis.
I don't know why I didn't call 911 from my cell phone or my SIL's home phone, but I went next door and called from the neighbor's (I suppose I wanted to get out o the house).
The 911 operator asked if I was sure she was dead. I said yes, she was cold and had livor mortis (I thought I might have to explain how I know about this from crime forums!). But the 911 operator wanted me to perform CPR anyway. So I went back over to my SIL's, called back 911 from my cell, and I had to do CPR until the paramedics arrived. [So if a bystander had called 911 about Cooper, they may have told him to do CPR even though he was obviously dead.]
The sheriff and a chaplain came. The sheriff asked who the next of kin was. I don't remember if the sheriff offered to do the notification or not - I remember I said I would drive to my niece's house to tell her in person.
The house was a comfortable, but not hot temperature. There was no air conditioning. Time of death was estimated to be 24-48 hours earlier. There was no discernible odor at all. [No comparison to Cooper's case here.]