Between this question and the corresponding DBA.SE question, there is a tremendous amount of ambiguity here. It's still not very clear what you're actually asking, but you have something of a question in this "I wonder how I can change the CS to make it available for Windows Authentication login rather than Mixed Mode ..."
To address that: Mixed Mode includes Windows Authentication and, as such, requires proper permissions management. I try to guide this sort of permissions management toward Active Directory Groups. You can add groups the same way that you add users. This is covered here. From there, you can set permissions by group (keeping in mind that DENY
trumps all other permissions).
To check if Mixed Mode is enabled (and to enable if necessary), check out this answer.
Please do not upvote if useful. The reality is that this question is a dupe of something already on the site, it's just a matter of figuring out what that dupe may be.