IPad Car Charging

The iPad uses a 10W charger. The iPhone has a 5W charger. Most older computers only support the original USB spec of 2.5W USB port power support. Your iPad, when on, uses more than 2.5W, so it will not charge unless it's turned off, and when off it will charge at less than 1/4 the speed of the normal iPad charger. That can be up to 16 hours for a fully depleted iPad.

Newer Apple computers, and computers that support USB3.0, support higher USB power standards, but if your computer doesn't then you'll need to invest in a new charger for your iPad.

Note that the iPad will generally charge off other USB chargers from other manufacturers, but only at a slower rate than the original iPad charger, unless the charger you use is specified to charge the iPad. When the original iPad came out 10W USB chargers were not common.

No

I mix and match my chargers often, the only disadvantage is that the iPhone charger charges slower according to a lot of sources, but I have yet to experience it. I still have an iPhone 3G charger I use as a spare at work to charge my iPad on occasion.

Interestingly I have never noticed my chargers getting hot either, but will admit I have never actively looked.

Looking at the Charging Tips here the reason for the slower charge is that the iPhone charger is 5W compared to 10W for the iPad, based on wattage alone, I can't see how you would damage the iPad, I would suspect using a higher wattage might however.