1) Yes, you can use the nook as a storage device on the mac when you plug in with supplied cable.
2) Should be but I'd use the one that came with the nook
3) No, but I'd restart the nook .

I'd charge the nook with the supplied cable/charger not via the computer which can vary electrical supply greatly. The iPad one is built for the iPad. I'd suggest using what B&N supplied to charge it.

No other adapter will work with the Nook Color but the one that it was shipped with. It has the Nook horseshoe on it. Being connected to your PC to my knowledge does not charge the Nook.

I have tried other other USB cords and none work on the Nook.

I've used my apple adapter with nook usb cable. The cable is generic - my son uses it with his pantech laser phone.

That being said I would use the equipment you go with the nook, especially if you are having problems!

Could be the Apple will work but I've tried others and they will not. It will look like its hooked up but it is not.

I have several generic wall warts at 5VDC (industry standard for lithium battery charging). None work with the Nook Tablet with or without the Nook Tablet cable. I suspect that the BN design engineers have used the 5th pin in the Micro USB plug/socket as a decoder of some kind to lock out the generic cables and chargers. Thus the PC 5VDC going to the USB pin 4 will probably only partially charge (or not charge at all) the nook and the nook cable will not pick up the decode message from the charger when the cable is pluged into the PC. therefore the only way to get a complete charge to the nook table it to use the Nook Tablet wall wart and its BN cable. Moreover, those of U that have a USB socket in your car radio or car dash asray will also find that its 5VDC will not fully charge the nook tablet. Finally, it looks like the data lines in the charging/sync cable (pins 2 & 3) are NOT impaired by the BN efforts to force its customers to use their accessories. OBTW BN sells a NOOK Tablet car charger with cable for $25. And be wary of EBay and Amazon vendors that advertize compatable chargers and cables because they are proably not electronicly compatable.