First let me qualify myself as anything but an expert on an Ipad. My wife has an Ipad II and she was having some of the same problems with youtube and facebook.....they worked fine on Safari but not on the Ipad app. We final fixed the problem when we updated the operating software. To update the IOS we had to sync it thru my lap top to the apple site. I would have thought that the Ipad would automatically update the operating software, but obviously it didn't. It took about an hour to update but it fixed all the problems we were having. Also, make sure you clean off all the apps running in the back ground periodically. To do that double click the little button on the face side. The apps will show up at the bottom, then select one of the apps and hold it until it starts to shake. You can then delete them. One other thing you should do maybe once a week or so is to reboot the computer. You do that by pressing the little black buttton on the edge and the button on the face side at the same time and holding until it powers down.
If you already know all these things, I apologize.