I looked at the screen shots and here is what I think is going on:
First, your connectivity model is not correct as the local and minor roads are in their own connectivity group and DO NOT connect the major roads, highways, etc. If you want to
maintain these two groups, you will have to create a junction feature class and bring that
in and have it span the two connectivity groups. I suggest you look at the Paris data in
the network analyst tutorials for examples.
This would explain why your service area crosses over the highways. That is, they are not connected to the local roads and the service area sovler will not know they are even there.
Second, it is not clear how you have defined the restrictions. How is the evaluator set up? Your screen shot on the attributes has a restriction field set to all 1's. Does that mean all roads in that connectivity group are restricted? That would explain why you get the message that facilities are located on non-traversable elements.
Third, your network dataset says it is not built. So perhaps you made some changes and have not built it again.
Hopefully you can fix the connectivity, build and try again.