Yet another reason the IRS is demanding that schools issue a 1098-T showing how much was spent on qualified expenses and whether or not you were a full time student.
In order to continue claiming you as a dependent if you are under 24, the IRS doesn't care about your income, but your total support. If you did NOT support yourself, they can still claim you. If you DID support yourself, they can't. Once you are their dependent, they can claim an education credit, but which kind depends on the fulltime status.
To determine total support and whether or not you supplied more than half, use IRS.GOV, get publication 501 and do the worksheet on page 20.
As far as insurance, they can cover you until you turn 26 on their policy--if they want to. Lies may make them less interested.
As for lying about flunking, talk to them. My family made vacation requests and hotel reservations for one graduation only to be told the week before, oh, I'm not graduating. No one was happy. My job requires me to put in vacation requests in advance (many are doing it right now for all of 2013).