For paratroopers you can have a new unit, or simply let bombers (or Heavy Bomber) transport Infantry.
As for unit representation I think each land unit is a division.
So 1 infantry piece = 1 infantry division (10,000-20,000 troops.)
1 tank piece might be 5000 tanks.
And 1 fighter piece might be 1000 planes.
The proportions aren’t prefectly realistic of course.
Most incorrect being Carrier / Planes combination.
1 carrier piece carries 2 fighter pieces.
But in reality one fleet carrier can only take 50-100 planes.
Japan only had 10 aircraft carriers at beginning of WWII.
The game represents that with 3 carrier pieces.
So each carrier piece is like 3 aircraft carriers, carrying maximum of 300 planes (which isn’t 6 air divisions).