How the setitimer in linux is working in low level ? . I know its usages . What is the maximum timeout we can give to it ? . Will it respond to the system time (which we can set by date command) . For example : I give the timeout as 18 hours to setitimer , and increase the system time by 18 hours using date command , will it expire immediately ?

While a timer could certainly be set for "many thousands of seconds from now," that would IMHO not be a very good use for this facility. If you need long-term scheduling, use a facility such as cron, its many more-clever replacements, or the facilities built-in to systemd.

If you abruptly change the system's current-time, then obviously this would trigger a helluva lot of timeouts ... but, once again, this is really not a prudent thing to do to any system.

Interval timers are usually used to implement "polling" facilities that might go off, say, once a minute. They might also be used for "watchdog" timers, designed to allow a facility to realize that it might be stalled. The scenarios that you describe are really not within the scope of their intended uses.