If the murderer burned the body in one barrel it would likely stop burning well as it piles up, like a stuffed camp fire, so eventually they would very likely move parts out and resume the fire.
The boyfriend could have deleted messages as he went through them, pressing the delete number which everyone knows as he went through inconsequential messages, instead of waiting for the messages to end or pressing the skip number which people don't usually know by heart.
The single key being found instead of the whole set; it's possible she had only a single key or that the murderer kept only one needed to drive the car and got rid of the others along with the rest of her belongings.
For the boyfriend to kill her, he would have had to carefully plan it all based on her timed visit to Avery, and get away with it.