Are there other, non-Islamic sources that can corroborate either Abraha's elephant refusing to advance or the alleged giant flock of birds?

In short, no. These stories have the quality of a folk tale, there might be some element of truth to them but we have no verifiable outside information that anything like them ever occurred.

That being said, we do have corroborating evidence about Abraha and his expedition from Yemen towards the Hejaz.

The Encyclopaedia of Islam entry on Abraha explains this quite well, so I'll quote it at length:

ABRAHA, a Christian king of South Arabia in the middle of the sixth century A. D. In Islamic literature his fame is due to the tradition that he led a Yamani expedition against Mecca (referred to in the Kur'an, cv) in the year of Muham- mad's birth, c. 570 A .D . The details of Abraha's life given by Muslim historians are largely stories of folk-lore origin which have been attached arbi- trarily to the name of a famous personage. For authentic information we must turn to Procopius and the Himyaritic inscriptions. According to Procopius, Hellestheaios king of Abyssinia ('L'SHH of the inscription Istanbul 7608 bis) invaded South Arabia a few years before 531 A.D., killed its king, C appointed a puppet-ruler named Esimiphaios (SMYF of the inscriptions), and retired to Abyssinia; subse- quently, Abyssinian deserters who had remained in South Arabia revolted against Esimiphaios and set on the throne Abraha, originally the slave of a Byzantine merchant of Adulis; two expeditions sent by Hellestheaios against the rebels were unsuccessful, and Abraha retained the throne; Justinian's attempts to incite Abraha to attack Persia were in vain, for he merely marched a little way northward and then retired; so long as Helles- theaios was alive, Abraha refused to pay tribute to Abyssinia, but agreed to do so to Hellestheaios' successor. Our main epigraphic source is Abraha's long inscription on the Ma'rib dam (Corpus inscr. sent., iv, 541). This records the quelling of an insurrection supported by a son of the dethroned Esimiphaios in the year 657 of the Sabaean era (between 640-650 A.D.); repairs effected to the dam later in the same year; the reception of embassies from Abyssinia, Byzantium, Persia, Hira and Harith b. Djabalat the phylarch of Arabia; and the completion of repairs to the dam in the following year. A further text (Ryckmans 506, see le Museon, 1953, 275-84) discovered at Murayghan, east of the upper Wadi Tathlith, records a defeat inflicted by Abraha on the c North Arabian tribe Ma add in 662of the Sabaean era. The Ma'rib text begins, "By the power and favour and mercy of God and His Messiah and the Holy Spirit (rh qds)'\ It is perhaps significant of asec- tarian distinction that Esimiphaios, who was no doubt a Monophysite like his Abyssinian patron, uses a different formula, "In the name of God and His Son Christ victorious and the Holy Spirit (mnfs qds)"', possibly Abraha had Nestorian leanings. The titulature adopted by Abraha is identical with that of his immediate predecessors, "King of Saba and Dhu-Raydan and Hadramawt and Yamanat and their Arabs in the plateau and lowland", but in the Ma'rib text he calls himself in addition zly mlkn *g'zyn. The word *zly is not found elsewhere, and no satisfactory explanation of the phrase has yet been given. Conti-Rossini's rendering "the valiant king, of the (tribe) Agazi" is syntactically improbable; and Glaser's "viceroy of the Abyssinian king'.' is incompatible with the passage later in the inscription where Abraha receives an Abyssinian embassy on the same footing as those of Byzantium and Persia. J. Ryckmans' proposed reading *tly rnlkn "the king's highness" is worth consideration. From here onwards reliable sources are silent, and we have only the probably legendary story in the Islamic sources, which attributes the motive of the Meccan expedition to Abraha's jealousy of the Meccan sanctuary and a futile attempt to substitute his church at Sana as the place of pilgrimage for all Arabia. If Abraha really made such an expedition (the Kur'an does not name its leader), a more likely explanation of his aims is that the rapproche- ment with Abyssinia under Hellestheaios' successor caused Abraha to adopt a more aggressive policy towards Persia, and the expedition was the first move of a projected attack on the Persian dominions. However, it proved a failure, and only provoked the Persians to their invasion under Wahriz a few years later, which finally destroyed the ancient South Arabian kingdom. The Martyrium Arethae asserts that Abraha was placed on the throne by the Abys- sinian king Elesbaas (usually identified with Pro- copius' Hellestheaios) immediately after the death of Dhu Nuwas. Other ecclesiastical sources, such as the Leges Homeritarum attributed to Gregentius bishop of Zafar, give similar accounts. This version of events, which conflicts fundamentally with both Procopius and the inscriptions, must be regarded as unhistorical and due either to a confusion of names or to a falsification for polemical reasons.

As the author (AFL Beeston) notes, the Qur'an itself doesn't mention Abraha or his purposes. The details surrounding the Sura, that this was the year of Muhammad's birth, of Abraha's expedition, of the attempt to replace Mecca, all of this comes from either the hadith or the exegetical material. The verse itself simply reads:

Hast thou not seen how thy Lord dealt with the owners of the Elephant?

Did He not bring their stratagem to naught,

And send against them swarms of flying creatures,

Which pelted them with stones of baked clay,

And made them like green crops devoured (by cattle)?

And that's all we've got. Again to sum up, there are reasons to find elements of this story as plausible and some aspects are corroborated by contemporary documentary sources. But in general, to your points 1. and 2.? If you want to treat those as being entirely fictitious you would be on safe ground in doing so.