New battery installation in the Macbook Pro
It is a new battery.

The cycle count is a chip on the battery it self, if you move battery from one Mac to another the cycle count goes with it.

You only have about 2 hours left because you are consuming  3324 mA (which is high consumption). That value can go up is you reduce the consumption.

Fully charged Capacity is 8391 mAh. (new battery have that)

That value goes lower over the life of battery.

Charge reaming 4730 mAh. (this also tell you the battery charge status) in %. (56%)

That value will drop with the speed that depends on consumption.

You do not need 3D party app to find out about your battery.