I am importing an iPod external battery from a supplier from Hong
Kong. The supplier's company is in Hong Kong, the factory is in China.
 The external battery comes with a power adapter that is used to
charge the battery.  The package of the product (a card) has printed
"Made in China" and my US company's name.

My Questions are:

Does the power adapter have to be UL approved in order to enter US and
sell to the public?  Currently the included adapter is CE approved.

Does the external battery has to have "Made in China" marked on it? 
Currently only the package has such info.

Is there anything I need to be aware of in term of marking/labeling
when I sell this external battery to the public?