For those of you who aren't fortunate enough to live above the 49th parallel, in the CSIA methodology, a lot of emphasis is made on effective goal setting. Meaning, setting a goal that is achievable, and quantifiable. So saying "I want to ski better" isn't very helpful.
"I want to ski moguls in control" is something that we can work with though. Take that goal and break it down in to little morsels. One bump at a time. Get an idea of one thing to work on in each turn. Alpine Canada says that constant positive feedback is bad, but I think it helps the adult intermediate stay confident that they're on the right track. Take each bump, each turn and treat it as a small victory.
But if your goal is "I want to ski better, and I want to ski better now!" then you're going to be disappointed and end up selling your skis at a ski swap.
Another thought: You have to actually be willing to change. Back when I did my Level 1 cert, there was a fellow on the course who was probably a 55 or older intermediate who got argumentative when the course conductor tried to correct his skiing, and ended up blaming the conditions for an inability to adapt. If you come in with a blocked mind, you can't change, and if you can't change, you're not going to improve!
Anyways, looking at the questions in the OP:
- What helps the most to go from intermediate to advanced?
Mileage! As much mileage as possible, but with an idea of what to work on when you're getting that mileage.
- What difference does the region someone skis in make?
In the West, and anywhere that gets powder for that matter, it's easy to get a pair of huge fat skis and ski power and crud simply by plowing through everything without actually needing to improve your ability. But there isn't a pair of skis that will make skiing icy groomers dramatically easier. So people on the East Coast have a greater opportunity to improve technically. However, for people who just want to ski powder "better" maybe getting the proper equipment is going to be all the improvement they need!
- Does it matter how often an older intermediate can get on the slopes?
It depends. If an older intermediate takes a lesson then never skis until next month when they take another lesson, they're going to plateau. Hell, even an advanced skier who is actively working on something won't progress very much if they spread the ski days out too much.
Fear is a big detriment. One of my favourite students was this lovely 13 year old, who was in my camp group. Her mom would drive her and her younger brother to ski lessons and hang out in the lodge doing work until they were finished. That 13 year old is now a 17 year old instructor, so I see her mom a lot, and I always ask, why doesn't she learn to ski? Her kids love it, but as a working single mom, she's terrified that she'll get hurt and not be able to drive the kids around anymore. Now the chances of getting hurt are relatively small, and you could easily get hurt doing any manner of other things like walking across the street, but that fear is going to hold you back.
So what you need to do is let go of that fear. It's a good limiter and keeps you from doing anything completely insane, but you look at 8 year olds, and they have none of it! That's why they'll happily race down a mogul run in a wedge without turning, laughing all the way. It doesn't occur to them that they could crash. Hell, some kids like to crash for fun!