Can’t answer for aviation but I worked in the general testing and certification industry (Underwriters Laboratories) with tons of rules and externally audited standards about calibration of measurement and test equipment.

Yes, things like rulers and gauges are tested. The schedule depends on the use case and frequency of use. For relatively light lab duty stuff, rulers and gauges were checked 1-2 times a year. Things that are used more frequency or more aggressively are checked more often.