I'm positive that they know whether or not she was behind the Facebook posts. Facebook will readily turn over IP addresses if there is a warrant, and I can't imagine she is smart enough to hide her IP address. All they have to do is compare the IP address used between her account and Charlie's during the same timeframe.
Even if TK was behind the Facebook and trying to frame NN, there's no way he could make his IP addy match hers. So if her account matches CDC during that timeframe, it's definitely her.
As far as the phone records go, I'm on the same account as my husband, and for some reason Verizon won't ever talk to me without his permission because he is the main person on the account. It's actually super frustrating and condescending. So I definitely can believe that NN was having trouble getting any cell info from the company, she probably wasn't even on the account.