Could you perhaps provide more context? From the sounds of it, she is absolutely 100% wrong. Jews were definitely not considered German or Dutch or Slav and by the same logic would definitely not be considered Finns. She's so wrong I don't even know what to source, basically any academic textbook on the Third Reich would explain this clearly.

Finland, though in the war on the side of the Axis, was the one country the Nazis hardly ever even approached on the Jewish question.

To my knowledge this is correct. There seems to be no solid evidence that Nazis even asked for Finland to hand over its Jews; one conflicting account is from a Finnish-born former personal doctor of Heinrich Himmler, who claimed to have saved the Finnish Jews through his scheming. This claim is, suffice to say, somewhat hard to believe.

As I mentioned in my previous answer (with sources!), unfortunately this didn't mean that Finland did not cooperate at all with the Germans in this matter. There is evidence for the deportations of 51 Jews, 12 of whom were civilians and the rest prisoners of war. However, it is unclear to what extent them being Jewish was a cause for the POW's deportation; the case of civilians is clearer, and it seems likely that at least most of them were deported precisely because they were Jews.

However, this cooperation did not result from overt demands; rather, they seem to have been the work of small-scale antisemitism combined with a passion for bureaucracy and a desire to please the Germans. There is some belief that the deportations were linked to German food aid, without which there would have been famine in Finland in 1942/43; not in any official manner of course, but rather as a quid pro quo. I think there is some truth to this claim; certainly Finland in 1942 was in no position to displease the Germans overtly.

Despite that, the Finnish prime minister at the time answered to Himmler, when the latter brought the subject up in a meeting, that "Finland has no Jewish question" which was the end of the matter. The evidence also strongly suggests that aside from right-wingers and Nazi fellow travelers - who remained a minority - most politicians in Finland were very averse to handing over anything to Nazis; and after the debacle with first deportations, either whisked remaining refugees to safety in Sweden or issued Finnish citizenships to those who wished to stay. To my knowledge, no Finnish citizen was ever deported or extradited for being a Jew; the deportations hit only those who had been residing as refugees. (Not that it makes much difference, mind you.) Unfortunately, Soviet POWs did not receive the same consideration.

I've heard that Hitler did upgrade his opinion of Finns from semi-Slavic or Mongolian untermenschen (in the 1930s, there was a popular theory that Finns were basically Mongolian descent) to full-blown "nordic Aryans" after their performance in the Winter War, which obviously required them to be part of a better race. Could it be that this has carried over to Arendt's writing?

I believe, she is getting at the concept of an "honorary aryan". This sort of title has extremely loose meaning. An example of this, I can think of, would be in the movie Anne Frank; Diary of a Teenage Girl. When the Nazis invade the attic, one Nazi officer discovers Otto Frank to have a military trunk from WW1, he questions him as to why he didn't register as completing service on his documents and makes some comment that if he did he "would have been treated decently". The historical accuracy of this conversation is questionable, and very well could not have been real - but it is a good example of such.

However, these sort of decrees came from people who were outside of what the Bureau of Race Research would consider European Aryan race, ie Indo-European. I don't believe they would have considered the Finns to be part of this, as they were considered Scandinavian. You could counter this argument though, because Russia was not apart of the Aryan race concept and Hitlers sole reason for wanting to invade the Soviet Union was that the Bolsheviks were just a bunch of Jews running the country, and saw such as a threat.

I have read that the Germans approached Finnish authorities on the subject, but were rebuffed with the argument "there are no jews in Finland".

I have seen two interpretations of that statement - one that the jews were Finnish citizens first and jews second, meaning that there are only Finnish citizens in Finland - which their secondary indentity was did not matter, they were Finns.

The other is that the Finns referred to the 1795 Swedish law (which they were allowed to keep when they became a Grand Duchy udner the Russian Emperor) that forbid jews to settle in the country - jews had not been allowed to settle, thus there were no jews.

Another state that German authorities contacted Finnish authorites, in some sources President Ryti, in some Marshal Mannerheim about "solving the jewish problem in Finland" and got the short and firm reply "Finland does not have a jewish problem".

Finland did turn over 86 jews to Germany. 12 of them were refugees and accused of crime and arrested and turned over to German authorities. 74 were Soviet prisoners of war and turned over together with the about 3 000 Soviet prisoners that the Finns turned over to the Germans since they had a severe shortage of food and did not want to feed a lot of prisoners. The Germans in turn turned over Soviet prisoners of Estonian, Ugric, Finnish and Karelian extraction, which the Finns hoped to recruit to their army.

About 300 jews served in the Finnish armed forces, and 3 recieved the iron cross (all of them medical personell that served German wounded in northern Finland). All refused to take the medal.

Another question for anyone who knows enough to answer: In my textbook, there is a map of Jews killed per country in WW2. It lists Finland as having 7 Jews killed. How did they know only 7 were killed?