Don't be worried at all about taking the back off the phone. My i9300 used to lock up very frequently and the only way to reboot it would be to pull the battery...and hope. Since I switched to a custom ROM I have not had it lock up once but that's another story.
You can try apps like Greenify to increase battery life. If you are want to get real geeky you can flash your ROM to something suited towards conservative power consumption.
There is always the chance that what you buy on Taobao is fake. Be sure you pay through Alipay (I think....my wife handles this stuff not me). The seller won't get the money until you confirm the product is in good working order and is what you paid for.