How is the moon rendered partially red?
That's actually how it looked to the eye (roughly; the photo is a little bit brighter and more vibrant). It's an interesting thing. The center of Earth's shadow is a dark coppery red, but the edge of it (still umbral, not penumbral) is brighter, as well as bluer because of the effect of stratospheric ozone. So there's quite a brightness and color gradient across the Moon during the total phases of the eclipse, and especially when the Moon is hugging the shadow's edge.
Here's another wide-angle shot to give some perspective. The Moon is still fully in the umbra, but the edge is bright and over-exposed.
How visible was the mountain to the naked eye in the aurora or Milky way shot?
Visible, but not nearly as clearly as in the photos. Mostly it was the bright snow that stood out. These were pretty dark skies (
Bortle Class 3), and the surroundings seem virtually black for the few minutes until your eyes adjust.
Also, the aurora looked
extremely vague to the eye, and I could not detect any color besides perhaps the faintest hint of green toward the horizon. I didn't even realize it was the aurora (thought it was artificial light pollution, like a distant searchlight or something) until I took a long exposure and saw its full extent and color on the LCD screen. The eye is very bad at picking out color in low light environments. Their movement was also too gradual to notice without keeping track for a few minutes.
I'm guessing you live very far north if you're talking about the stars not being visible in May?

I'm at 48°N, which is just far north enough that the sky doesn't get fully dark for the week around summer solstice.
High latitude is the enemy to Milky Way photographers. For one, the bright central region doesn't rise as high above the horizon, and then when it is at its highest you have the least (or even no) darkness. At 50N you have to aim for a month before or after solstice. At 60N you need two months. The position isn't ideal then, but you can still capture interesting parts of the galaxy.