The bike sign means "cycleway". It tells bicylists that this path is designated as a cycleway and that they need to use that instead of the main road.

Pedestrians are allowed to walk on any highway (except motorways and trunk roads), including cycleways.

When there is no sidewalk, pedestrians are expected to walk on the road side.

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There are lots of safe ways to cross the road. In Denmark there are no rules about only being allowed to cross roads at pedestrian crossings. People can cross almost anywhere they please - by law.

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This is NOT a motorway. It is a normal country road.

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The lack of pedestrian traffic_signals does not mean that pedestrians are not allowed to cross there. It is solely a cost saving measure, as only few pedestrians are expected here.

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You don't need to run at all. Denmark is not a car prioritized country. When the light is green you are allowed to start crossing. If it turns red while you are still not finished, the traffic from the other direction have to wait until you have passed.

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You should not map to fit navigation systems. You should only map what is on the ground; what is the actual reality.

The reality here is, that there are no signs telling you that foot=no