When one is working for a repair station, one is working under the repair station certification, and generally does not sign off a repair using one's own certificate number.
No type certification is required (or available) for aviation maintenance technicians in the US. The FAA has been rumored to be initiating such action at some future date, but this has been a rumor for a very long time.
The Inspection Authorization comes with an expiration, and it can be renewed in several ways; either by work experience, or by attending biannual training.