I the Magyars seem to have passed through Kiev; were the Kievan's at the time under Varangian rule? (I've read about the Varangians setting up governments over the local Slavic peoples, whether by request or not, I'm unsure).
And prior to their migration, did the Magyar come from nearer the baltic coast, or did they originate nearer the Arctic Circle. Their language's closet European relative is Finnish, but they're considered Uralic languages, did they perhaps come from nearer the Ural Mountains?) I misread/remembered this. It's Urgic, not Uralic, but the language group seems to straddle the Ural Mountains, and seems to be part of an larger language tree known as Uralic
Bonus question: What spurred their migration? Many cultures pushed west from the steppes, and at different times, such as the Huns. I've read as well that some Hungarians claim their culture descends from the Huns, in some way, and that the city of Buda (before becoming Budapest) was named after Atilla's brother Bleda), could their migrations be related, even if 300 years apart?
There were certainly some contacts between Varangians and Magyars. Magyars were mentioned as part of the Imperial bodyguard in Constantinople in the middle 9th century and since the Magyars were in almost constant contact with Byzantium regarding many varied military matters it would be impossible for them not to have interacted with the Varangians.
There are also several recently discovered examples of Magyar made luxury precious metal items in Varangian graves along both the Don and Dnpr river systems. The Magyars controlled these areas in the 9th century according the latest archeology to come out of Russia and Ukraine, so the Varangians must have had some mutually beneficial arrangement with them.
Their interests probably didn't conflict very much since the Magyars' domain was the steppe and the Varangians' the river. As far as Kiev is concerned it does not seem to become a major power center until the Magyars leave in the 10th century. Kiev was a very unremarkable place in the 9th century Kiev, little more than a village, and probably under Magyar rule or tribute since there are so many Magyar finds all around the area.
As to the migration route, the most recent finds in Russia and Ukraine show the Magyars in the Southern Urals at the edge of the steppe and the forested steppe in the 7th century. By the 8th they are part of the Khazar empire and reside further west in the middle reaches of the Don and Dnpr. By the middle 9th they are joined by the Kazhar rebel tribes and form a tribal union absorbing them and they are jointly over the Carpathians at least in temporary military groups.
As with all steppe groups it is very difficult to actually trace their steps before they enter into the archeological record as a distinct group. Before the 6th century or so we might be looking at an ethnogenesis that involves some kind of turkic military reorganization and influx because of military vocabulary. It's very foggy but we know some things, for example Magyar and Finnish split about 1000B.C. Around the same time Magyar picks up basic Indo- European Sanskrit words pertaining to steppe lifestlye so they might have entered the steppes around this time.
There are also a lot of Alan loanwords and Scythian that was added to Magyar after those languages formed, so that suggest further steppe cohabitation, but there are no Gothic or East Germanic loanwords which possibly means they didn't participate in the Hunnic invasions. They might have pulled north in front of the Huns and then joined with a turkic group in the 5-6th century to emerge as we see them as identifiable Magyars.
Bonus Answer: Historians are divided about what spurred their migration. Some hold the opinion that the Magyars were defeated by the Pechenegs and had to migrate to escape them. This seems highly unlikely to me for a number of reasons.
The move was very organized and involved moving women, children and the elderly but most importantly vast herds of animals and precious metals. The Magyars had a string of military successes for almost a hundred years and they became the land superpower in Europe for a time. They utilized an incredibly sophisticated logistics and command structure with rigid discipline in tactical battles. It doesn't add up with the idea of fleeing migrants in my opinion, but who knows, maybe the pressure from attacks on the steppe forced them to get hyper organized. Another telling fact is that tribes were voluntarily joining the Magyars as their successes mounted both before and after they arrive in the Carpathian basin which also doesn't play into the refugee narrative.
Lastly, as far as the Hun-Hungarian connection goes. We do know from the recent archeology that widespread culturally Hunnic settlements can be found in modern day Austria, Bavaria, Czech Rep, Slovakia and Hungary. We also know that many of these settlements continue well into and after the time the Magyars settle there.
While there is absolutely no proof the invading Magyars were descended from the Huns, they made up only about 20% of the local population after they arrived. The other 80% was made up of various people who settled there before the Magyars arrived including large groups of Huns who had long lost their Hunnic identity by the 9th century.
So modern day Hungarians are about as Hunnic as the Czechs, Austrians or Slovaks, which is to say not very much since the cultural identity is dead. Genetically they certainly play a component and many people in Europe carry 'Hunnic' genes, although there truly is no such thing since Huns were a pure political construct with no genetic basis.
Fun Fact about the Physical Anthropology: About 1% of 5-6 century Hunnic skulls have predominantly aisan features, 15% show a caucasian/asian admixture wile 84% are European.