This is me, catching up (computer and connection issues).....
As to TRO3085, I honestly don't know about that era as well as I do pre-3060, so I don't feel comfortable commenting on it.
I will have to defer to those with a better understanding of internal FWL politics, but as to the Lyrans, although there will be serious graft and corruption on a regular basis, as it becomes clear that that there is an impending dust-up after Kerensky's pullout, there will be a rapid movement to get things fixed, and quick.
In re infantry motive power, most of the main House infantry units will be motorized or mounted on hover vehicles at the very least...with the proviso that unless we're talking about elite units, most "infantry" are likely to be little more than glorified, heavily-armed police. (This will NOT be the case inside the TH.)
Other than commando's, very few units will use actual parachutes for insertion...but actual Jump units will be largely for show.
Certain specialist units - mountain troops, or jungle units - will almost certainly remained foot-bound.
A good resource for bicycle infantry is "The Bicycle in Wartime", by Fitzpatrick:
http://www.amazon.com/Bicycle-Wartime-Illustrated-History/dp/1574881574 -- "Smart" infantry will use these. "Most" infantry will not.