CET1 isn't specific to Fannie & Freddie, it applies to all financial institutions.
The GSEs can't offer new Preferreds unless they want to pay Dividends to existing Jr. Preferreds. Unless of course they can sell new Preferreds with no Dividend for 2-3 years (who would buy that?).
But even then, those Preferreds would not count towards CET1 as per the definition of CET1.
No, because he doesn't define what CET1 means. It's part of Basel III. You can check the full definition in Section 1240.20(b), starting on page 312 of the full capital rule.
FHFA even included a chart of what counts towards what kinds of capital on page 15 of their capital rule fact sheet.
By HERA Calabria has to propose risk-based and minimum (what he calls leverage) capital standards, and the latter can only be met with core (tier 1) capital. What should be telling is that Calabria did not have to include a CET1 capital standard, but he did it anyway.
That's a huge tell. It means he wants FnF's capital structure to not be too pref-heavy. In fact, footnote 34 on page 45 of the full capital rule says (emphasis added):
Ideas of a mostly-pref recap need to be thrown in the garbage where they belong. Calabria would not have included a CET1 standard or that specific quote if he was okay with FnF not having their capital raises be mostly common shares.
Calabria said "It has always been my view that an exit from conservatorship is going to require a large capital raise by Fannie and Freddie." and "The shareholders will be heavily diluted when we raise capital." I'm not sure how much more clear this can get. We can argue all day about whether or not a mostly-pref recap is possible, but Calabria's words and documents show a clear, ahem, preference for having the capital raise be mostly, if not entirely, common shares.