How can you do better in the press conference. She only only said "it didn't go that bad"
When asking questions to Dana at the beginning, focus on attack-related questions (so you have better answers for the questions that the reporters ask during the press conference). Charles usually errs on the side of providing too much information, so the more factual your answers, the better they'll go over with the press.
Note that new questions may show up during your conversations with Dana based on what you've already picked. So visit a menu again even if you think you've already selected all of the relevant things in it.
(Dana is also pretty good at letting you know what items are relevant to the upcoming press conference.)
An indication that you're doing well during the press conference is that Charles will raise his hand in an apparent thumbs up.