FIRST has always allowed teams to sign up for as many regionals as they want to attend (that number currently being a maximum of 7 due to the impossibility of the same team competing in two events during the same week).
As for the 3rd
District event question, Jim Zondag just put up a whitepaper with the answer at
http://www.chiefdelphi.com/media/papers/2804. If you haven't read it, you might want to, as this is one of the FAQs for FiM.
Whether or not there should be a limit to the number of events a team can attend other than the calendar limitations, and how a district system allowing more districts than the number counted should deal with a number of teams in eliminations who can't get points (and are presumably blocking out others who need the points to get to State/Region Championships), are currently wide open questions.
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Past teams:
2003-2007: FRC0330 BeachBots
2008: FRC1135 Shmoebotics
2012: FRC4046 Schroedinger's Dragons
"Rockets are tricky..."--Elon Musk
