Standalone ATmega clock continuous lifetime
So how long will my clock run if is it supposed to be online 24/7

Until you turn it off or a stray neutrino corrupts the flash memory, or the flash memory degrades (20-100 years or so depending on temperature).

Should I reset it sometimes? If yes , when, after how many days should I reset it?

No.

And do I need a coolant system for it? (I guess not)

No. Not unless it's in a sealed container with no ventilation and a hot environment.
However
Your RTC-less &quot;clock&quot; will probably not be particularly accurate, unless you have some external source of time (NTP, GPS, etc) as the Arduino's internal timing is not very accurate, and built on a breadboard it's even less so due to excess stray capacitance.