I’m sorry I did not see this sooner. Jordanes is the focal point of my research and I do so ever enjoy discussing him.

First off, the matter of Jordanes’ origins has been oversimplified in Mierow’s translation. Without getting too knee-deep in Latin, compare Mierow’s translation with Mingarelli’s more literal interpretation:

“Let him not believe that I have added anything which is in favour of the aforementioned people, as though from them <my> origin derives, other than what I have read and knew for certain” (2018, page 9).

We can see how ‘quasi ex ipsa trahenti originem,’ is not as simple as Mierow makes it out to be, but he’s not wrong per se in his interpretation. Mingarelli, and most of scholarship, do agree that Jordanes was Gothic to some extant (Goffart 1988, 22; Søby 2002, 84-93; Goltz 2008, 268-269; Mingarelli 2018, 7; this is not exhaustive). So while Mierow here is not being literal, he is, I think, right in his translation.

This is where matters get murky: there is a textual issue dating back to Mommsen’s Monumenta Germaniae Historica, Auctores Antiquissimi, 5,1 (“Getica”), 1877. This edition is, for now, the most widely accepted (though it has errors which even Mierow corrected before translating; for an alternative edition starting to make ground see Giunta and Grillone 1991 or Grillone 2017). In the passage referring to Jordanes’ lineage, his father is called, ‘Alanoviiamuth’. This has led many to suspect that there was a textual issue and really it should read something like, Alanovii Amuth ‘the Alan, Amuth’ (Søby covers this matter well 2002, 86-90, 91-92). Regardless, we cannot corroborate the spelling in the manuscript Mommsen used, one of the oldest and most reliable, because it was completely destroyed in his library fire… sigh. Anyhow, the matter of Alanovii Amuth brought about much speculation surrounding Jordanes also being of Alanic origin. Really, it’s something of a moot point because in this period of Late Antiquity, the ethnic lines between groups truly began to blur (see Meier 2017, 338-340). This means that many Goths were of Alanic decent just as many Alans were of Gothic… and so forth with other tribes.

Whatever Jordanes’ ethnic origins, Goffart really hammers this home, Jordanes was thoroughly Byzantine (1988, 22, 32).

Your second question, the purpose of Getica, is still uncertain. There are three major camps on the matter: the positivists, the skeptics, and the independents (see Mingarelli 2018, 21, who carves them up). These camps are also, incidentally, centered around how faithfully Jordanes copied Cassiodorus (I won’t go too far into this but certainly can if you wish). Suffice to say, Jordanes in his preface records that Castalius asked him to abridge Cassiodorus’ twelve histories of the Goths, a work that no longer survives. Jordanes then says that he could only get a hold of the work except on a three-day loan. Naturally, he could not do what Castalius asked. Still he says he tried to and has retained the sense of the deeds if not the words. Now, to the camps: the positivists contend that Jordanes faithfully abridged Cassiodorus, having been familiar with the twelve histories before Castalius’ request to draft Getica. Thus he was able to fulfill the request, one way or the other. Naturally, those in this camp would see that the purpose of Getica was to abridge the twelve Gothic histories (they often refer to Jordanes as Cassiodorus-Jordanes). The second camp, the skeptics, contend that Jordanes’ supposed abridgement of Cassiodorus’ histories is a fabrication in the pursuit of propaganda (especially argued by Goffart 1988). Goffart, for example, contends that the purpose of Getica is to create a new sense of peace and order between the eastern Romans and Ostrogoths, the latter having been conquered by the former. The final camp, the independents, believe that Jordanes tried to abridge Cassiodorus but was unable to due to many factors such as, but not limited to, time constraints and his overall familiarity with the twelve histories. This camp, nevertheless, would say that at first he tried to abridge but ultimately produced a history so that he had something to give to Castalius (Van Hoof and Van Nufellen 2017, is going to be especially important for this camp). I’m sorry I, nor anyone, can definitively answer your question on the purpose of Getica.

Your third question, whether it was a bid to integrate Goths into the empire, is discussed but it cannot be concluded. We just don’t know enough about Jordanes to say anything one way or the other. Your fourth and fifth questions also follow the same problem. Ultimately, we don’t know who Castalius was, what sort of relationship Jordanes had with Cassiodorus, and we don’t have the twelve Gothic histories written by Cassiodorus so we don’t know why Jordanes wrote Getica, who he wrote it for, and to what extent it was an abridgment! (Kulikowski is good if you want to learn more about the abridgment issue and the matter of his drawing from oral history, 2008).

That said, it is certainly the case that what was produced was, in part, mythical, historical, and propagandistic. The mythical aspect certainly came, to some extent, from Cassiodorus’ Histories (see Heather 1993 and Søby 2002). This is seen in Jordanes’ telling of the three Gothic ships from Scandza (Getica 94-95). The historical aspect came about once Jordanes was no longer able to draw on the twelve histories, thereby resorting to Greek and Latin works to bolster the ‘abridgment’ (Van Hoof and Van Nufellen 2017). The propagandistic elements of Jordanes’ work are more difficult to identify. It was certainly the case that Jordanes was critical of Justinian while supportive of Belisarius in his work Romana (Kruse 2015) which may also be detectable in Getica (Whately 2013). He may have had an anti-Gepid attitude which colours his accounts of the Gepids (Mingarelli 2018). Finally, though there are many more examples, he may have been partaking in a long debate coursing through Constantinople on various matters which involved, but was not limited to, Zosimus, Marcellinus Comes, Procopius and, perhaps, John Malalas (Bjornlie 2013). It is also the case that Jordanes drew on propagandized evidence (Amory 1997). Getica is something of an odd beast that floats somewhere between real and fabulous.

As you can see, nothing said about Jordanes is certain. In fact, everything we know about Jordanes comes from Jordanes. No one else in antiquity mentions him in any significant detail (as far as we know). Hope this helps!

Edit: Spelling mistakes.

Edit 2: date error on citation.