A: 

I found the answer myself.

In the app.config there is a section security mode="None", and on next line... transport clientCredentialType="None" proxyCredentialType="None" realm=""

I changed this to mode="TransportCredentialOnly" and ...clientCredentialType="Ntlm" proxyCredentialType="Ntlm" realm=""

and it started working!

We found this suggestion here: download.microsoft.com/.../SP14EntSearchDev_QryAPI_1.docx

//Lars S

Lars S