Once you have added a cohort using ZiLink - Cohort Sync, ZiLink uses a process to check new cohort enrolments and will add the teacher(s) for that cohort automatically. The process runs every few hours so if you need a quicker teacher enrolment use a manual enrolment to do so. ZiLink will catchup and you will see a ZiLink teacher enrolment in the enrolments list. You can leave or delete the manual enrolment - it will not make any difference to the user, their data or experience.
Enrolling users at category level - yes you can but if you enrol individual users ZiLink will not be able to manage them when, for example, a student is moved from one group to another in SIMS.
It is not possible to enrol an existing cohort at category level but you can create a cohort and add individual users to the cohort. Also, Moodle recommends using Cohort enrolments rather than enrolling users at category level. There is mention of performance issues relating to category enrolments at this link http://docs.moodle.org/27/en/Category_enrolments.