You are buying into a bogus history in so many aspects.

First, the Sephardic Jews have a totally different story. They were in Spain at least in the First Century AD, enjoyed a long "golden age" until the Moors kicked them out in the 15th century. Most went to North Africa, now most are in Israel.

https://www.chabad.org/library/article_cdo/aid/4095674/jewish/Ashkenazi-and-Sephardic-Jews.htm https://www.britannica.com/topic/Sephardi

Second, Khazaria just referred to an area and "Khazarians" were wanderers. You are off by 600 years in their organization as some sort of state.

https://en.wikipedia.org/wiki/Khazars https://www.britannica.com/topic/Khazar

It's quite safe to say that by 700 AD when they adopted Judaism as a state religion to foil the Christians and Muslims who were both pressing the Khazars to take a side in their own fight, that there were already plenty of real descendents of Abraham from the middle east already there, as by then there were real Jews not just in Spain but all over the known world. After all, they had already been forcibly relocated to Egypt, Babylon, and Persia, and were all over the Roman empire, and from all those places they had spread out and settled. This is attested in a very reliable historical book, the Bible, e.g. the Book of Acts, Chapter 2:

5 And there were dwelling at Jerusalem Jews, devout men, out of every nation under heaven. 6 Now when this was noised abroad, the multitude came together, and were confounded, because that every man heard them speak in his own language. 7 And they were all amazed and marvelled, saying one to another, Behold, are not all these which speak Galilaeans? 8 And how hear we every man in our own tongue, wherein we were born? 9 Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia, 10 Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes, 11 Cretes and Arabians, we do hear them speak in our tongues the wonderful works of God

So the Khazars had real Jews already, they adopted the Hebrew alphabet to their language and became literate, and the official religion was Judaism: however, in their legal system there was a separate court for each major religion, Christian, Muslim, Jewish, and pagan, so it seems plausible that those who chose to practice Judaism did so in real faith, not coercion.

As to this star business... In ancient times, not just in Mesopotamia but everywhere, the stars, planets, sun and moon were associated with deities. In Mesopotamia particularly, stars were used in graphics to indicate gods and goddesses, just as haloes in art indicate saints. Some early stone carvings had a 4 pointed star like a little diamond. The Sumerians were big on 8 pointed stars and their cuneiform image for "god" is an 8 pointed star. Six points was a somewhat later style and use was widespread, not exclusive to Remphan. It was used, and still is, in Islamic art, and was used in early synagogues and Christian art too, especially around Galilee. This relates to a Bible prophecy, "the star which will come from Jacob." Here's a little real archeology on the topic: https://www.youtube.com/watch?v=Qrv1_C-I3Es

Not really used by the Jews until the 17th century. Not an object of worship, just an emblem. Kabbalistic tales about this star are as good as this fairytale, in which you note the Seal of Solomon is a pentagram, not hexagram, which binds and dispels demons. Worshipping Remphan is briefly mentioned at the bottom as something you shouldn't do. https://en.m.wikipedia.org/wiki/Testament_of_Solomon

Slightly more detail about Remphan and the two references to him in the Bible, along with some etymology, is here. This article concludes that the most we can say about Remphan is that he was an idol and should be rejected. https://en.m.wikipedia.org/wiki/Remphan