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no you don't have to but if you want to use it while it is charging then you can
Yes, you can use it while it is plugged in.
If it is an iPod Touch, yes, you can work on an iPod or use the iPod while it is charging.
Of Course! You can preform any function on a phone while charging, including calling and texting!
because you use it while its charging
Most of the time, yes
It can, and using it while it's charging won't hurt it, but sometimes it's difficult to use the Kindle Fire while it's on the charger. This may depend on your version of the Kindle, but there are some that are glitchy and difficult to use when they're being charged.
If you are charging your device on a laptop or desktop, your charge time will be much slower. From a wall plug, it will be faster.
Yes you can - it will just take slightly longer to charge.
By definition, Bluetooth is wireless, so no you cannot. There are USB headsets with cords that you can use with your PS3. The official Sony headset does have the ability to let you talk while it is charging in the charging cradle.
it doesn't matter.
Yes just like the Dual Shock 3 Controller