No, only if you have some kind of terrestrial TV set up or if you watch Live TV online via BBC's iPlayer or one of the major channels' live TV players.
Yep, and the rules are absolutely mad. You can watch at home or on the go, provided you're on battery power. As soon as you plug your iPad or iPhone or whatever you're watching iPlayer on in somewhere else, the address the electricity is being supplied to needs a TV licence.
I get that these warts and things appear over time, and it's probably not intentionally the case that whether your iPad is plugged in or not can determine whether your licence covers you, but rather to avoid people creating fixed 'TV viewing installations' in other people's houses and claiming their licence should cover it, but still...