I posted a comment, but the comment window is either closed or the admin has to review it. Either way, here's my take:
The girl with the missing tongue was assaulted by another member of the team.
At some point during the night, there is a heated argument between this girl and some other particular member of the team - the dispute turns violent inside the cramped tent; which is cramped enough that she cannot quickly exit by conventional means, so being cornered and out of options she frantically slices her way out and runs outside, followed immediately by her attacker, and not far behind the entire rest of the team, doing their best to calm/resolve the situation.
Dyatlov quickly places the flashlight atop the tent thinking that the chase won't take more than a hundred yards or so and then everyone will promptly return to the tent. This point is crucial - had some large event taken place that caused the entire team to flee as in an emergency, the team leader would have without question taken the flashlight with him. He instead left it as a short-distance beacon.
The chase drags out for over a mile until the girl can run no farther, and the attacker finally is upon her with a knife (perhaps her own) and proceeds to remove her tongue. The team then wrestles with the attacker in complete darkness, which results in four of the group falling into a ravine and dying instantly.
The remaining five now have no idea where they are, and immediately plan for survival; They quickly build a fire and set up an impromptu camp. There are a few different ways the story can progress from here (the least experienced stayed behind and the most experienced tried to trek back, some died quickly so the remainder then left for the tent, etc), but in the end, they simply didn't know how far they were from the tent, or even what direction they were in relation to it, aside from "downhill". This would indicate that it was dark enough that they couldn't see their own footprints in the snow.
I'd attribute the snow on the one side of the tent to be a simple snow drift on an unmaintained tent. It's clearly not enough to be a small avalanche, and even if it were, the team wouldn't have run that far.
The radioactivity that was found wasn't enough to cause burns or even create a symptom of its being present, which would indicate that it was very low-level, which could be attributed to anything; In an era where pottery and watch-faces were highly radioactive, having an article of clothing that registers modestly on a Geiger counter would probably not be so unusual.
The orange skin and white hair would most likely have something to do with the mortician - even if their hair were white when they arrived, the mortician would have the option to dye it. That he didn't would indicate some error or aesthetic taste on his part.