"Do you know why late October can be a month with more chances than late November?"
I defer to an expert, who quotes info from NASA in question #2: https://www.aurorahunter.com/aurora-borealis-faq.html
That said, aurora can appear anytime, all year round. Depends on activity on the sun. Of course, when there's not much darkness at night, not much opportunity to see them. That's why in Alaska they can't be seen during the summer until after mid-August (Land of the Midnight Sun).
"I think it is also a matter of luck too."
Yep! I've seen many a forecast fizzle. My favorite site is this one: http://www.softservenews.com/
As for Denali in winter: https://www.nps.gov/dena/planyourvisit/winter-activities.htm . There are a couple of places in Healy that stay open all year, and if you're interested in dog sledding, this is a highly rated tour: https://www.earthsonglodge.com/winter.html . You can see aurora almost as well from Denali as from Fairbanks. It's about a 2 hour drive from Fairbanks. However, if you've never driven on ice or snow, you might prefer to stay in Fairbanks and play it by ear if you venture out on the highways. Check the daily weather forecast, Alaska 511 for road conditions, and always take an emergency kit along in case you slide into a ditch or the car breaks down. It doesn't cost a lot of money to put one together, and it could save your life. Here is a recent thread on the subject: https://www.tripadvisor.ca/ShowTopic-g28923-i349-k10056934-Winter_driving_supplies_readiness-Alaska.html
"would you recommend to rent a car "
Well *I* would, but then I'm used to driving on ice and snow, lol. But I do suggest you rent a car for at least 2 or 3 days--at that time of year you should be able to get them for about $30 a day, plus tax and insurance, so not a lot to spend even if you don't use it. You can decide on each day if the roads are in decent shape for you to drive. Keep in mind no one was born knowing how to drive on ice, we all had to learn, and we learn only by doing. If there is ice/snow, try to find a large parking lot and practice braking, accelerating, and turning. Just remember to do everything in slow motion: start slow, stop slow, turn slow. Any sudden changes in speed/direction might send you on a scenic 360 degree tour!
EDIT: BTW, you might enjoy checking on the aurora cam at Churchill, Manitoba: http://explore.org/live-cams/player/northern-lights-cam . I enjoy clicking on it from time to time, and you can scroll back for up to 4 hrs to see what you've missed. They have consistently amazing displays. The only nights I haven't seen aurora there have been the nights that were cloudy. Though I don't check every night, I'm sure some nights have nothing.
Edited: 6 years ago