The widget you're looking for is called
WheelPicker and as always, there's
already 3rd party libs just for this. Have a look.
In landscape mode the list should appear on
the left half of the screen with a selection band
that is vertically centered.
This could easily be done using appropriate
On the right half is a button, which will act
on the selected item in the list. The first item
in the list should be in the center. That means
the list is infinitely scrollable.
Again, appropriate styling and
I suggest you delve into the source of that
WheelPicker and see how you could
tailor it to your liking.
Hope this helps!