The first one is I think just the router treating the red path as prohibited to cyclists. Change the mode to *foot* and the red path will be used. So I think its just the absence of bicycle permission on the path that's causing that.

The second one is a question probably best asked to Valhalia, because both graphhopper and OSRM are happy to route that way. The only clue I can think of is that node 2500860968 connects to a way marked access=private but the node itself is not marked private, so that shouldn't stop bikes being routed along the cycleway.