She was very strange in her jokes about the TV and Charlie. Even if that is true, why bring it up. She appears to be thinking out loud, but I believe it’s an act or she’s nervous and overwhelmed and the only information she’s worried about retaining is her “story” or alibi. So, she repeats the tv repair with detail, the liquor store, with detail. Fails to ask specific questions about who, what, when and how someone shot Dan.
And I also agree with you about the cop car. Why on earth would she say such things to the officer about her brother?? Just seems odd and I honestly think she was spinning because they caught her off guard by bringing her in for questioning so quickly. She likely thought she would find out later.