Approx./approx. are documented shortened forms of approximate/approximately. This is a style-and-abbreviation question rather than a universal punctuation law.
Dept/dept. abbreviates department. Cambridge shows periodless and period-ending forms across its dictionary varieties, so the useful rule is to follow the relevant regional or organizational style consistently.
Est. is a documented abbreviation with more than one common expansion. The page distinguishes meaning, capitalization, and punctuation rather than presenting one context-free rule.
“No.” is a conventional abbreviation for “number” in Chicago-style contexts. The guide keeps it distinct from the number sign and from shortened forms such as num. or n., which may carry other meanings.