I really want to use SQL-server from a C#/.NET appliaction without using SQL-Server accounts or adding the affected computer to the same domain or to any domain at all or to use the same logon-name as the domain.
Isn't there any way? Did someone try to do this using the MONO implementation of SSPI?
To rephrase your question, you want to use domain authentication without domains.
No, that's not possible.
You can set them each up on domains and use trusts between the domains, or you can use SQL authentication.