The type of feedback I got the most was that I'm not able to 'advertise' myself and my project.
Every interview is a sales pitch. The famous book, studied widely at military academies around the world, The art of war, by Sun Tzu, states that if you know your enemy and you know yourself, then in a thousand battles you need not lose once.
When applied to sales or job interviews, it requires one to thoroughly investigate who is being pitched to and clearly articulating the value you are proposing in a short period of time.
Therefore, I recommend studying how you can refine your pitch from a well rehearsed academic presentation at great length down to a two minute pitch and even better to an elevator pitch.
By focusing on the most important value proposition your skill in "advertising" yourself and your project will improve.
I hope that answers your first question about how to best prepare for your interviews. I believe that if you start with a good pitch, The questions of the interviewers will then naturally go deeper into the content, instead of the other way around. My guess is that you are providing too many details, The interviewers are getting lost in the details and not seeing the bigger picture value of your work.
To answer question number two regarding training. I would start by familiarizing myself with the work of Steve Blank, The creator of NSF Innovation Corps. He has excellent presentations and videos, but this blog post seems to address but I believe is your issue directly. https://steveblank.com/2010/04/22/turning-on-your-reality-distortion-field/