To play it by ear means that, let's see, you improvise. You don't follow a plan. So Miller's going to go into the negotiation without his notes. He's not going to use a plan. He's just going to react as things happen. To blow your own trumpet means to boast about how great you are. In the last dialogue we had time to face the music,. It means you accept the negative consequences of your actions. For example, if lots of people are angry about a decision you made and they're all angry, you need to just go in there and speak to them. You need to face the Music.
Learn some English music idioms in this funny episode. Transcript and vocabulary available here https://teacherluke.co.uk/2009/11/07/music-idioms/
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