Well, no, there was no such 'caste structure', unless you take the folklore of Rígsþula seriously and literally as a depiction of Viking Age society being composed of three different races of thralls, karls and jarls. That's not really tenable. Iceland had never had a king in the Viking Age. People are only sporadically referred to as jarls in Viking Age contexts, and it seems to just be a term for a noble without prescribing any role. In Sweden the term doesn't seem to come into use until the late 12th century and peaks in the 13th, and is abolished by the end of it. (so the Swedish medievalist Dick Harryson's novel "The Century of the Jarl" takes place in the 13th century) The earliest medieval law codes of Scandinavia don't recognize 'jarl' or even nobility with a legal status; there are only free men and thralls (and often a distinction is made between debt-thralls and others) "Nobility" in the Viking Age appears to be little more than the richest of the farmers.

In other words, Rígsþula seems to reflect the 13th century society it was written down in more than the far older society it's supposed to be. Later scholarship has tended to favor a 13th century date for it, the language is archaic, so there are some who think it might be Viking Age in origin. In any case it is obvious it's literature and has to be treated with great care to draw any conclusions about society from it.

With that out of the way, did they respect foreign nobility when it came to slave-taking? Perhaps or perhaps not; Laxdæla saga has Melkorka, an Irish princess taken as a slave and sold to a buyer not aware of her noble background. The historicity of Melkorka is pretty dubious though, this is a family saga and being descended from slaves who were secretly nobility is of course a lot cooler. In Ynglinga Saga, a Swedish king Agne defeats and kills a Finnish chieftain and takes his children as slaves, and his daughter Skjálf as a wife/concubine. However she tricks him into getting drunk and hangs him to his death as revenge. Here too, a 'high born' foreign slave is still perhaps more than the average slave, while in the story of Geirmund Heljarskin, a slave Leif is passed off by a queen as the son of the king, yet revealed later by his un-noble nature.

These stories do not say much either about actual slaves or nobility as they do about contemporary Scandinavian prejudices about them. Generally, slaves are other - physically different, ugly, foreign, dark, small, cowardly and stupid. Reality is different though; law texts and other things imply that slaves are not always physically distinguishable from the free men.

It was a common practice among viking raiders to ransom captured people. It gave cash money and which much easier to transport home, for starters. It does not really make much sense in that context to take a VIP as a slave, because he or she could be ransomed for more than he or she was worth as a slave.

For the most part, slaves seem to have been foreign, and certainly treated as foreign 'others'. Even freed slaves lived with a stigma for the rest of their lives. As for debt slavery, that was not something were forced into "technically", it's presented as a choice on the part of the debtor, not a demand from the creditor. It's not clear whether they were treated better than other slaves, but as said they did have some rights others didn't. Those made slaves because they'd committed crimes however, were little better.

Foreign slaves are treated differently than native ones in the Gulaþing Law of Norway. (however we can't blindly assume these laws were the same centuries earlier when raiding was going on)

AFAIK there's no text that speaks of other Scandinavians being taken as slaves after a battle. Most such battles are between kings anyway. The battles that lead to the most slaves being taken were slave raids against; preferably done against the most defenseless people. It seems that slaves were more often sold in a nearby slave market than transported the whole way to Scandinavia. Slaves sold in Byzantium were likely captured along the way, not brought from home. The historian Stefan Brink thinks the amount of slaves that were around in Scandinavian societies of the Viking Age has historically been greatly overstated:

".. the custom seems to have been either to take them as hostage and then ask for a large ransom, or to sell them at some slave market. The bringing home of slaves to Scandinavia was certainly a fact, but in my opinion only on a small scale; probably the slave was seen as a precious commodity, to show off. I think slaves were fairly uncommon in society."

In short though: The enslaving of foreign nobles seems to be romantic myth more than something that actually happened. It doesn't really make any sense to take as slaves people who could more easily be ransomed for greater profit. Although the Scandinavians, unlike some Mediterranean societies, did not have slaves that were solely foreign others, it does not seem they enslaved free men of fellow Scandinavians who'd merely lost in battle. Scandinavians were worth more as people.

(Literally. Äldre Västgötalagen specifies the penalty for murder of a Dane or Norwegian as 9 marks - less than for fellow Götar or Swedes, but more than Germans or Englishmen where the penalty is 6 marks. For a slave it is 3)

Stefan Brink, Neil Price; The Viking World, 2008

Ruth Mazo Karras; Slavery and Society in Medieval Scandinavia, 1988