Does the timing of jumps matter?

Indeed, timing the jump is important as well. If you jump too early (while in the ramp), your jump will be higher but won't advance horizontally too much, and if you jump too late (just in the border of the mountain), the jump won't be as high.

Imagine that the jump kind of moves you in the direction you had just in the moment you jump.

Some characters (like Maya) simply have trouble with chasms, and sometimes it's simply too difficult to avoid falling. The best you can do to help them crossing is to have the flying suit.