No, it's not possible for brakes to go from fine to not working at all in 3 months. They probably did some multipoint inspection before sale - ask them to see that and find out what the brake wear was. They would normally also check the braking efficiency during an inspection, so ask to see a copy of that and the one they have now done to determine that your rear brakes don't work.
More likely, Pulsars seem to have an issue with excessive handbrake travel and it needs about 10 minutes work to adjust it.
As for potential death traps, most of the force of your brakes goes to the front wheels, so it's not been as risky as you think.
I would be wary of the dealer telling you that the brakes need replacing at some astronomical price and that the warranty doesn't cover them. If they do anything other than say that they'll sort it out at no charge, tell them that you wish to reject the car and look forward to receiving a refund.
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