Tell me about Khazaria. Are the European Jews descendants of them or did they come from Palestine?
No, Karaites are the descendants of Khazars: https://en.wikipedia.org/wiki/Crimean_Karaites .
>>2676495
Pavić stated that the Khazars were a metaphor for a small people surviving in between great powers and great religions. In Yugoslavia, Serbs recognized their own fate; it was the same in Slovenia and elsewhere, a schoolbook on survival. The same in Hungary and Czechoslovakia, and on and on. A French critic said, 'We are all Khazars in the age of nuclear threat and poisoned environment.'[5]
The ashkenazis are partially descended from them
Read this for an overview of the (potential) Khazarian conversion
http://www.jstor.org/stable/10.2979/jewisocistud.19.3.1
A far as genetics go, European Jews seem about half Levantine, half European. Doubt they have any Khazar ancestry at all.
As for Crimean Karaites and their connection to Khazars: no one really knows at this point, perhaps in the future.