Specific users should see files of my private repository

Is there a possibility to make branches of a private repository visible and/or editable to other users, who are registered or not registered at github? Can I invite them to a read and/or edit a branch or a file of a branch?

No, if you give them read access to a repository they can read the whole repository, with all branches and files. Regarding write access you can use protected branches to limit where people can push.