Yes the boards will agree, but it will be because FHFA tells them to. The "interest of shareholders" thing doesn't apply while FnF are in conservatorship.
For Treasury this is correct. FHFA is not responsible to either of these.
No it isn't. Private parties (individuals and companies) will be buying the shares. The proportional ownership is for their use, not the government's. Therefore all takings and illegal exaction claims will fail.
All lawsuits based on this idea of yours are frivolous and won't affect any part of the decision-making process.
And if you somehow end up being right and you can stop the secondary offering by filing a lawsuit, all you're doing is preventing recap and release. A retained earnings-only recap is not going to happen.
Also, Calabria and Mnuchin are far too smart to give possibilities for a recap that are illegal. Both a secondary offering and a junior-to-common conversion are 100% legal, and any challenges brought to them in court will just be a waste of the plaintiffs' and the government's time and money.