charging in power off
You can charge your iPad 1 while in power off mode.

With regard to using a Chinese non-Apple branded charger, this is possible. However you should be aware that Apple's chargers are recommended. The price difference between a non-Apple branded charger and Apple's own charger is significant; that difference is because of Apple's design costs and additional safety features.

Ken Shirriff's article showing the inside of an Apple iPhone charger demonstrates why the price difference exists.