Youtube is no longer integrated with iOS. You can download the app fromt he app store.. it's designed for iPhone... but states that it works with iPad.
As for running slow... trying holding down the power and home button at the same time for 10 seconds to do a hard reset.
Also.. if you double tap your home button it will bring up a small window across the bottom of your screen... this is called the multitasker.
Hold your finger one of the apps til they jiggle... then tap the red minus button to kill the app. If you kill them all this should help your ipad run alot faster.
Good luck 😀