OK... (nice start)
1. On your larger mountains, place white behind the black lines, on the shadow side, keep the lines black, but use a dark gray-blue fill color.
2. Canyons - well to match your design style, I'd use a solid line to denote the top of the canyon on both sides with a box canyon rounded end or pinched end, then short dash lines from "top of canyon" line inwards towards the bottom of the canyon. (Look at my May Challenge entry at the north side of the creek, see the short embankment. Do it like that on both sides of canyon and it should work out.)
3. Yes, grassy plains or savanah, that gets less rain becomes desert. Many plains areas border deserts of the world. It is definitely geographically possible.