About Testament, there's something that called my attention. The first succubi appeared as a crow and her original appearance because Testament is freed from Justice's control? (since we saw that she appeared as an EXE Beast in Missing Link). And the 2nd (from Strive) where did she come from?
We don't know their official names yet (though I casually refer to them as PINK and BLUE respectively).
They seem to be able to swap places with Testament at any given moment… (particularly during Possession/Warrant).
The implication is that Testament merged "his" existence with EXE Beast's and "they" are all one and the same vessel… so PINK and BLUE are probably an extension of Testament's vessel as well (either as part of the blood contract, or simply merged with Testament's existence).
Rather, it seems to be the case that PINK and BLUE are "offspring" from the original EXE Beast, so in fact you could technically classify them as Testament's children.
The details are rather hazy right now, but it is certain that the original EXE Beast had the ability to transform in to "Calamity One/Arbiter Sign" (EXE Beast "jaws") as well as the small Crow familiar (Unholy Diver).
So it would only make sense that PINK and BLUE both have the same abilities as the original succubus EXE Beast.
As for the origin of EXE Beast herself... it was sometime after Testament’s defeat at the hands of Kliff Undersn in the year 2140, when Testament was nearly mortally wounded by Kliff during their last fight during the Crusades.
At the time, Testament was, as he put it “a low level Gear”, so merging his existence with EXE Beast was his way of increasing his powers so he could get his revenge on Humanity (and Kliff, which he later killed during the faux tournament in 2180).