Also, was Ethiopia or the land that modern Ethiopia occupies or the civilization from which a line of continuity can be drawn back from modern Ethiopia towards into pre-Christian times a Jewish or Jewish-influenced state?
Sorta. On the first bit, there was a Jewish kingdom in the region, but I wouldn't call them the leaders of Ethiopia. However, there was a large Jewish population in Ethiopia. They moved to Israel en masse in the early 1990s, but there was a significant population. And this population seems to have been larger historically--there was much coercive conversion to Christianity from Judaism earlier on. The relationship of Christianity in Ethiopia with Ethiopian Judaism is evident in works like their respective biblical canons--both Jews and Christians in Ethiopia have bibles written in Ge'ez, which contains books not considered canonical in either Christianity or Judaism elsewhere.
The rulers of the Aksumite kingdom appear not to have been Jewish at the time that Ezana converted to Christianity in the 3rd century.
Altars, tombs, and stelae at Addi Gelemo and other sites from the 5th century BC all depict a recurring symbol of a crescent and a disc. This crescent and disc symbol also appears in altars and coinage from the contemporary Sabaean kingdom of the southern Arabian peninsula. This symbol is believed to depict a Sabaean lunar deity.
The appearance of this symbol on both sides of the Red Sea does not appear to be coincidence. The current theory is that there was much cultural, technological and linguistic exchange occurring in the first millennium BC.
Why is this relevant? Because this disc and crescent symbol continues to appear in temple contexts, as well as in coinage into the early Axumite era (the first and second centuries AD). So, it is this Ethio-Sabaean lunar deity that looks to have been worshipped by the rulers of Axum in the pre-Christian period.
Of course, there are some indications of Judaism in the Horn of Africa region in the time period we are talking about. The Byzantine historian Procopius describes an Axumite expedition against the Himyarite kingdom (in what is now Yemen), and describes the Himyarite leader Dhu Nuwas as being Jewish.
Similarly, there is popular oral tradition of the queen Yodit ("judith") of the Beta Israel, who is remembered as the final conqueror of Aksum and is sometimes credited/blamed for the usurpation of the Zagwe dynasty.
Sources
Aksum, an African civilization of late antiquity
Foundations of an African Civilization: Aksum and the Northern Horn 1000 BC to AD 1300 discusses the conversion to christianity starting on p.91
African Archaeology, 3rd edition by David W. Phillipson. Discusses the Crescent and Disc symbol starting p.228, with a depiction of an altar at Addi Gelemo on p229.