What SM Specialty tracks is it ok to have a Cadet Assistant? As an example Admin Officer. Is it ok to have a cadet as a assistant? What would they be permitted to do within regulations?
Virtually any duty position can have a cadet as an assistant. Phase III and Phase IV cadets are supposed to be an assistant for some positions as part of the Staff Duty Analysis portion of the Cadet Program. See CAPP 52-14.
As for Specialty Tracks, cadets generally do not follow the Specialty Tracks, except for a few like Communications in order to get the Communications Badge. Most specialties do not allow cadets to earn the specialty badge, though.
Any position could theoretically have a cadet assistant except for an IG. As for your example, an admin officer could have a cadet do anything they do. A personnel officer is a little different though. Cadets should never have access to senior member personnel files, but could help with tasks such as updating a CAPF 66, filing participation letters, etc.
In regard to actually earning the technician specialty rating, as far as I know, only the Communications track and IT track allow Cadets to work towards them (I have the IT badge).
In the respective CAP Pamphlet regarding the specialty, there should be a section detailing what a Cadet must do to get said badge. (This only equates to the badge -- it doesn't confer the actual specialty track, and if the Cadet turns SM, the badge comes off unless he / she actually takes that specialty track for their personal development.)