'04 ZR2 questions

[bduff509]

(1) My heater doesn't shut off. At first I thought that the hot/cold selector worked a valve on the heater core but the dealer tells me that it's a door that closes off the air to it. He also told me that GM has no fix for this. He also said that all Blazers do this. Only problem is the door doesn't close. As long as I'm moving down the road I'm getting real hot feet. Does anyone know of a way to stop this?
(2) My Z has 3.73 rears w/265 tires. I believe this might have a lot to do with the nearly 10 mph low reading I get on the speedo. Can it be recalibrated to read closer to true mph?
(3) My tranny has been acting weird. When turning on to a road at about 15-20 mph & I hit the gas the engine races a little as if it were caught between gears. It shudders pulling out of stop signs, seems to slip pulling steep hills at low speed & takes way too long to shift into OD. About 4 sec. start to finish. Again, the dealer says this is normal. I don't buy it. I've had too many cars & trucks over the years that didn't act like this to believe that this is normal. Am I wrong ? Anyone else have this too?

Thanks in advance.