You can see how off the trace can be here: https://i.imgur.com/eHJI8FH.jpg . You could probably do some smoothing to help fit some of this to a street but I've been on runs where I zig zag down streets just to add distance or to do hills.
Wow, that's pretty horrible, must be giving you close to twice the actual distance. I think Google Maps on my phone applies some smoothing that does this a lot better, but then it can lag for a while when I'm going sharp right in an intersection.
Maybe try telling it that you're biking instead, my guess is they do more smoothing the higher speed they expect.
It's pretty much raw GPS if you're in walking or biking mode. Driving mode uses sophisticated filtering algorithms, and doesn't actually make any assumptions about your speed, though it does assume you're on a road.
I have a question for you. If GPS locations in cities are affected by reflections off buildings, wouldn't the effect be deterministic and could you take advantage of that to reduce the noise?