08 hhr water not moving fast enough, sluggish car dies if rpms up runs hot?

I fill 08HHR up w coolant. If 

it’s too low, it’s hard for engine to start (prob normal..?) then the water won’t move or move fast enough. (I think because I have to give gas and still trouble, also I give 20,000 rpm’s seems to move water faster but, water is shooting out of the weep hole from the expansion tank and shoots too much out? Is it possible that it’s the water pump? How can it be water pump if it’s still moving water?  I’ve changed the thermostat. Heat in the air blowing in front seat is changing with rpm’s as well