After i installed my amp every time when i start the car, the columbus(rns510) turns off and pops the speakers. then it turns on back again. Does this mean my battery is dead and have no energy to power amp + starter motor?

If the engine cranks briskly and starts immediately the battery is fine, the starter draws so much current from the battery that it's normal for other systems to temporarily brown out.

 

There are ways to mitigate this and there are videos online if you search.

Easy to get your battery tested at a garage, most will do it foc too......

 

Turn your radio off when you turn the engine off until you get to the cause........so it doesn't do any damage.

10 hours ago, MicMac said:

If the engine cranks briskly and starts immediately the battery is fine, the starter draws so much current from the battery that it's normal for other systems to temporarily brown out.

 

There are ways to mitigate this and there are videos online if you search.

it cranks, but the batt voltage drops to ~9.5v in the moment of cranking.  before installing the amp, the HU never turned off, and back on again.