I use powerbookmedic.com to find parts for Mac's based on Apple Model . It may require a little research but it should allow you to sort your feet out by model. Search based on Model # If I've helped please score!
No it doesn't look like it is. If you look at the breakdown guide for the iPad 2 on this site you'll see that its actually soldered to the logic board. It is apparently the Orange boxed one. Here is a link to the breakdown guide. iPad 2 Wi-Fi EMC 2415 Teardown If I've helped please score!!
From the internet. A non-charging battery can sometimes be caused by an overheating laptop. As the temperature rises, a thermal sensor shuts off the battery to prevent the lithium-ion polymer from becoming so hot it bursts into flame or explodes. While the unibody design used in the MacBook Pro and MacBook Air do a fairly good job of keeping everything cool, you might want to let the system cool down if it's warm to the touch. You might want to reapply your thermal paste. Are the fans working? heat sinks connected correctly?