Your first question is difficult to understand. I think you are referring to the component TBO (Time Between Overhaul) period? If the TBO on an engine or prop is (for example) 2,000 hours, then the engine or prop must be overhauled prior to, by, or at 2,000 hours TIS (Time In Service). Similarly, other components may be life restricted by either hours or cycles; e.g. the starter/generator, fuel nozzels, hot sections etc on certain PT6 turbines are life limited.
I am not aware of a maximum number of hours at which an airframe (in total) is "unserviceable". However, components of an airframe may be "lifed" - e.g. a maximum number of pressurisation cycles on a Beech King Air (after which the fuselage requires modification or retiring), or maximum number of hours on an Islander wing (think it is 26,000 hours?). Cessna 400 series wings were limited to 8,500 hours (again from memory) before the spar cap required replacement (Australia only).
Looking at Scramblers post, reminds me that an R22 helicopter is "lifed" at 2,000 hours, after which all components require overhaul.