As you know, I'm not a native speaker, but I want to say something about your first question. There was more difference between her "can" and "can't" than just the glottal stop at the end of the latter. The intonation was also different.
Unfortunately, that isn't always the case. Also, not every American will be kind enough to throw in a glottal stop there, which as you say is not that easy to catch anyway. I know from Americans that it does happen that "can" and "can't" confuse them (when stressed). These words can be indistinguishable even to native American speakers.