It's hard to respond to these questions without thousands of words, but I'll try some scattered responses to various points above.
From what we understand, all of your scenarios were true at various points. There are times when humans expanded at a lightning pace and times when we seem to have been at a standstill. We don't really know to what degree these are accurate reflections of the reality vs illusions caused by an imperfect material record.
One well-known obstacle to human expansion was the Arctic itself, which seemingly resisted human inhabitation (even by archaic humans) until relatively recently.
As for how fast we could have expanded, modern humans are incredibly specialized to rapid, optimized adaptations. Our language capabilities, high order thinking, sociality and other rapidly adaptive traits evolved at least partially in response to periods where climates could shift by tens of degrees in mere decades during the pleistocene. On top of this, the kinds of nomadic foragers that would have been these early pioneers live a lifestyle that's not only adaptive to variable environments, it's designed to exploit that variability. If the winter is going to be too cold in this valley, you move over to the next one. If there are dangerous animals too close, you pick up camp and go. You're using the resources from multiple environments as those resources are accessible, which allows you to exploit landscapes that any other lifestyle would find completely inhospitable.
Happy to talk more about any of the above in a more focused way.