Rated flow in the following is in conjunction with the rated lift meaning it can lift 15 meters at flow of 12 Liter/ minutes from a well? But what if its sucking water from the water company with existing flow rate. So the total flow rate is additive and is more than 12L/ minute, right? Or wrong? I plan to buy this pump and it confused me for days.
To fully answer we need a diagram of how this pump will be connected to the water company. I will speculate on a few configurations:
If the city water flows into a bucket at atmospheric pressure, and the pump pulls out of that bucket, it will just be limited to the performance of the pump as expected.
If the city water flows into the inlet of this pump; the users (sprinklers etc) on the outlet will see an increase in pressure. (~15m of water more pressure for your 12L/m) This configuration is typically called a "boost pump", because it boosts the pressure.
Increased pressure can mean increased flow, but the amount the flow increases depends on the the downstream user. For a sprinkler or some sort of orifice type restriction, the orifice equation gives us some idea. If the pressure at your sprinkler/user goes up by a factor of 4, the flow rate through that sprinkler/user will double.
Note that if the flow from the city water is higher than this 12L/m rating of the pump you will see less pressure boost, and at some point (say 24L/m) this pump will actually reduce the pressure (and the resultant flow) delivered.