IPAD2 is it compatible with Ancestry.com

If you mean the Ancestry App, it is not. Ancestry requires an iPad which can run iPadOS 14.1 or higher. An iPad 2, which is over 10 years old now, cannot run anything higher than iOS 9.3.5 or 9.3.6 if a cellular model.

Whether you can access Ancestry.com via the Safari Browser on your iPad, you'll have to try and see, but you most definitely cannot download the app to such an old device.