Is your secondary suspension arm is a skeletal mesh? As they do lag behind unless you move them in local space only. Otherwise not sure what is wrong. Can you show how you do calculation for animation?
In theory yes. But keep in mind that currently implemented Differential is a Locked Differential and for cars you need a bit more advanced version of it - Limited Slip Differential, which allows for differential to be open when there is no torque coming into the system and gets locked as you push pedal: https://www.youtube.com/watch?v=ujsxq9WBllU
Locked differential might work in principal for off-road vehicle, but you might have issue with turning it as wheels will be slipping not able to rotate with different velocities. For the tank it’s not a problem as there are clutches between track and differential.
Having said that, be aware that WheelAxle component was something that I’ve added very early in the development of the ModularDriveTrain and never used since, I don’t think it will work correctly. Instead, you could use TrackProcessorModular as a “wheel processor”, just make sure to set weight of the tread to something very small, like 1kg or less. Pretend that you are driving on sprockets 
Otherwise, you are correct. Information passes from engine down to differentials and track/wheel processor, here we calculate how track/wheel should rotate because of the engine torque and provide information about “desired” wheel velocity to friction component. Friction component tells back how much “reaction” force we should apply to the track/wheel (handled by track/wheel processor) because of friction and then data flows back to the engine.
I advise to always make backup before upgrading, but overall, new c++ implementation of components comes as new set of classes. They have their own category “MMT” in Add Component interface. So you can safely mix BP version with C++ version in the same project. Mixing it in the same vehicle might be difficult as base class is different.