Cycling involves suffering and intense physical and mental pain. Is it something you get used to?
What'd Greg LeMond say, "It never hurts less, you just go faster"? Something like that. Yeah, cycling is funny because there are so many levels of pain: lactic acid pulsing through your legs, the mental fortitude it takes to know you could always ease up...but you won't. Plus it goes without saying, there's not a lot of padding in spandex and pavement is very hard. Cycling is a vicious sport.
During an average day of racing a grand tour, how much of it is spent hurting and how much of it is fun and relaxing?
The days are long with four, five, six hours spent in the saddle. They can be rough, fast, and hard. But it's not like you're cross-eyed with exertion 100% of the time. The race starts out aggressively, that can be anywhere from five minutes or 50 miles; then there will usually be some sort of lull followed by some fast and furious in the final few hours. So to use proper cycling nerd vernacular, "in the pain cave," ohh, we're probably there 30% of the time. Then another 30% is what we would call fairly easy (but a sprint to the average bloke), while an additional 40% is just plain hard, but we'll call it just outside of the pain cave.
How unpleasant is a mountain stage?
That probably depends on who you ask. I imagine climbers, such as Chris Froome, like them more than the average person. The ebb and flow of a grand tour is funny though; some days you feel great while others you seem to be suffering start to finish. Sure, mountain stages are tough, but they're part of the adventure.