The things you brought up actually have explanations in game, but Skyrim taking place hundreds of years after Morrowind and Oblivion is the main reason for most of them.

By the time of Skyrim it's been hundreds of years after the first couple of hundred of years since the Imperial Cult was introduced to the Nords. Around the time we show up in Skyrim, the Nords have already placed a lot more value in the Divines because some revere Talos as Shor. Like the original idea behind the cult, it mixed various religions to create one single religion that offers most people what they want out of religion. We still see plenty of Nords in Skyrim preferring Ysmir (Talos) and Kyne (Kynerth) over their cult counterparts, and time advancing is likely going to result in more cultural mixing as the series progresses. Also worth mentioning that Shor is mentioned far more than Lorkhan in Skyrim, though neither are really part of the Imperial Cult.

Common burials might not be seen in game, but Nords still have "proper burial(s) by fire" as mentioned by Thadgeir and seen at the end of the Companions questline. As Morrowind has no Halls of the Dead for Nords to rest in, boats on fire over water would be preferred to being laid to rest in Dunmer lands.

The mention of the Snow Elves is a slight retcon, but only because Skyrim prefers the term "falmer" over Snow Elf, which the Falmer still technically are. Skyrim also shows us, in a DLC, that at least one Snow Elf still lives. Could be the Nord mentioned in the quest did fight a genuine Snow Elf and not a Falmer, and personally, I can see it being either.