Simple question??

Yes the ATV will mirror your iPad.

 

In mirroring

You likely can do that desired with ATV.

Not sure about iOS devices, but from, in example, a MacBook it is simplicity itself to mirror that on its screen to a HDTV via ATV. One must turn file sharing on from the computer, and have ATV recognize this, but simple procedures, and but done once. It does not matter whether iTunes or not, that on the small screen will be no less on the large.

As a note, mirroring is not the most elegant of solutions. Instead of an accustomed remote to pause and play and so forth one is tethered in using the computer.

 

Youtube app will airplay (non-mirroring) right to your AppleTV wirelessly. if you start playing it on your iPad, you just click the airplay button and it starts playing on your selected AppleTV. I do this daily.

Many apps have Airplay (non-mirroring) built in. For those that do not, there is mirroring which is like sending your iPad's "desktop" directly to the TV. This is how you can do videos from Safari IF there is no stand alone app.

 

Yes you can do it with any iOS device on demand. There are 3 steps:

1) turn TV to Apple TV input
2) open video on iOS device
3) press Airplay symbol, select Apple TV

-OR-

if you would like to mirror the entire iOS device's display:

1) Turn TV to Apple TV input
2) Open Mission Control (swipe up from bottom of screen)
3) press Airplay symbol, select Apple TV, select "Mirroring"

A select few apps will explicitly block Airplay and Airplay Mirroring due to DRM reasons, but they are few and far between. I believe HBO recently removed this restriction as did Netflix, but I'm not positive on that. Generally the restrictions are with sports related apps like ESPN, NFL Sunday Ticket, and a couple others.