We just have very few t-bars all of which you don't have to use, unless you really want to, the one up at Valluga being an exception, bear in mind that the t-bars are able to operate in all kinds of weather, where the chairlifts cannot, especially because most of the chairlifts are with bubbles.
As for the ski school, should you decide to put him in a group lesson, most of the instructors are non-German speaking, or quit good at English and the kids are divided up into groups according to age and ski level, just like anywhere else in the world.
A private lesson might be more the way to go, then you can split up the tuition an maybe ski for an hour together, at the end of the lesson.
Where to ski - well that certainly depends about the weather and snow conditions, there are plenty of runs that will suit a 7 year old boy. It's very easy to get to Zürs and Lech or Stuben, but don't forget the Rendl side of St. Anton has some lovely intermediate runs.
It can by quit crowed if you're here in the New Year week so some good planning and start early in the morning are some good advice.
Ask at your hotel and the lift company has an information service scattered 3-4 places over the St. Anton ski area, ask them and they will give you some good and informative advice.
I hope you'll get a lovely stay and come back to St. Anton in the future.