Shortest route

To get the shortest route, you will need to create a custom profile (a .lua file) where all roads are weighted at the same speed. The routing algorithm will then choose a 5-mile unclassified road (at 60mph) in preference to a 6-mile trunk road (at 60mph), whereas the standard car.lua will choose a 6-mile trunk road at 60mph in preference to a 5-mile unclassified road at 40mph.

You will need to specify the path to your profile in the command line when calling osrm-extract. I would recommend starting with car.lua and modifying it rather than creating a new profile from scratch.

As Andy has mentioned, I gave a brief overview of OSRM's profiles at https://help.openstreetmap.org/questions/30272/how-the-routing-osrm-algorithm-works .

This works https://www.openstreetmap.org/directions?engine=osrm_car&route=61.7141%2C50.7956%3B61.6808%2C50.8076#map=12/61.6972/50.8332

but if i extend the route south a small amount https://www.openstreetmap.org/directions?engine=osrm_car&route=61.7141%2C50.7956%3B61.6759%2C50.8092#map=12/61.6951/50.8095 the route takes the detour you have found. The obvious route your dotted one as a 60kph speed limit mapped the used alternative as no limit set. Maybe osrm calculates that as slower because of the 60kph

Note: this is not from first hand experience.

OSRM always only has one profile per instance, at least when it is run in normal CH mode. And, as far as I know, the standard setup optimizes drive time, not distance. In other words you would have to set up an instance that uses the travelled distance as the metric (which I assume is possible, bat may be not easy).