YES.
The drive is 6 hours. Google maps gives reliable directions, but most carriers may lose cell phone service on the way (it is picked back up in Lake City) so you should look at a map beforehand.
The drive is 4.5 hours. It will be beautiful but be prepared for mountain passes.
No, unless you plan on doing any of the bigger hikes. If that's the case, you have been warned that those roads destroy cars...
Denver is the biggest, closest hub (I realize 4.5 hours isn't that close). It is also possible to fly into Gunnison, CO, which is only a 1 hour drive from Lake City, but these flights are fewer and further between as it is a small local airport.