1. She is basically saying that the snack is woodlike (hence, can be used for paneling). It may be because the snack is tough or involves tree derived components, or both.
2. Dickey is a false shirt. If his wife was on the bottom of the lake with his dickey, that would mean she had grabbed it off him when his was pushing her into the lake.
3. Not sure, but it might be because high fiber food such as broccoli make one prone to gasses.