The altitude definitely has an impact. I live at sea level, but I visited Colorado Springs last year, which is somewhere around 6,000-7,000 feet. I didn't notice a difference on a level surface, but even just a slight incline at a walking pace and I felt like I was trudging through mud. And I'm in pretty good shape and I do a fair amount of incline running in my regular training.
I would expect that if you train at a high altitude, when you are at lower altitudes everything will be easier. Of course, if you live at altitude and are never at lower altitudes, this won't be terribly helpful. We went on a guided hike and, during the hike, we asked the guide, who was in pretty good shape, if she noticed that everything was really easy at sea level and she said she never really spent much time exercising at sea level so she didn't know.
Not sure about the training.
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