I'll try to help explain some of these things as best as I can to the best of my knowledge.
It is true that judges chose the winners for many/most of FIRST's awards on-site. Judges, though, do go to competitions with knowledge about your team and what awards you are most competitive for receiving. Teams are asked to fill out information on the Team Information Management System (TIMS) found at:
https://my.usfirst.org/frc/tims/
The judges receive all the information your team fills out prior to the event and use this information for the purpose of judging awards. Your team must fill out information concerning Team History, Team's FIRST Impact, Team's Strengths, Robot and Game Strategy, Funding Sources, Team Goals, Community Description, Most Significant Challenge Overcome, Most Competitive For Which Awards, and Public Awareness. The only way to access this is through the login that your team's Main Contact registered with. Make sure that someone on your team has filled out all this information, as well as the rest of the requested information on the site. Also make sure to complete the Chairman's Award submission to make sure you become eligible for the rookie awards.
Concerning how to prepare: your team may wish to produce any number of promotional pieces to implement and show to judges in the pit during an event. Such things would include newsletters, business plans, team yearbooks, pamphlets and brochures for team outreach programs, promotional videos, flyers and posters about your team, and so forth. All these can be highly beneficial in aiding to explain the functions of your team and how you have endeavored in succeeding in the various areas of FIRST. Teams can also prep by making sure all members of the team are highly knowledgeable about all the functions of your team as well as by designating certain individuals to serve as spokespersons.
And to your last question, the answer is yes. Teams may win the same award at any and/or all the competitions they attend (so long as nothing has changed from previous years!)
Ok, well I hope that helps! If you need anymore assistance, please feel free to PM me. Massive luck in all your endeavors!