The radio is under warranty, so have the dealer replace it. As for tires, well, that's not really the fault of the car. why did the tire go flat? We've had two flats on our 'rolla, both due to screws in the tire. But, lots of construction around right now, so it's not unexpected.
As for it rolling backwards on an incline, I can't recall right off if ours does that or not. I know our Subaru will roll backward on a hill (yes, it's an AT) if it's steep enough. Tonight I'll try the 'rolla and see what it does.