Inside of a gas water heater there is a plate on the bottom and a flue tube for the flames / hot gasses to run up and heat the water. By having the flame on with no water, all that happened was that the plate and flue tube get very hot, likely red hot. It's highly unlikely they were damaged permanently though, there are safety cutoffs that would have turned off the gas way before that happens.
As to the T-P valve, when you finally turned on the hot water, it likely immediately flashed into steam. A hot water heater tank is NOT a steam vessel, hence the T-P valve. the T-P valve is SUPPOSED to open and vent the steam, so it was actually doing exactly what it was designed for. Once it had cooled down it would have probably re-sealed, but changing it out is not a problem. It's doubtful that Sears would pay for it without having first given it a chance to cool and seal though.
Dents on the outside of a hot water heater would be strictly cosmetic. The dent you can see is just on the "skin" of sheet metal that is covering the insulation inside, between the actual tank and that cosmetic skin. I usually buy the dented ones to get the discount.
Don't call that plumber again though, that was a bonehead move on his part...