My question is exactly what is "backpressure"?  If I have a pumping system that has a discharge pressure of 100 psi and add a backpressure valve to the line that reduces the pressure to the outlet of the valve to 20 psi, will I have 80 psi backpressure on the pump?

To my way of thinking, the backpressure on a piece of equipment is the pressure immediately downstream of that equipment.  So if we consider a pump developing 100 psi, with a downstream valve just after it dropping it to 20 psi such that it has 80 psi pressure drop across it (ignoring other pipework etc. for simplification), the backpressure on the pump is 100 psi, and the backpressure on the valve is 20 psi.  
The same is true with relief valves - the backpressure is the pressure immediately after the relief valve.  When the valve is not relieving, this is static backpressure.  When the valve is relieving, this is relieving backpressure or total backpressure.

On the second question, the answer is generally yes.  With a centrifugal pump, the pressure will increase and the flowrate will drop to the point where the new system curve meets the pump curve.  With a PD pump, the discharge pressure will increase, and the flowrate will stay pretty much the same.  It might back off a little if there is increased slippage at the higher discharge pressure.

I think the best installations have a pulsation dampener on a vertical pipe run just after the pump discharge. If this is done a control valve and flow measuring device downstream can then be used to control the flow. Otherwise injection type flowrates are normally achieved by controlling pump speed (frequency), or stroke.

To help insure the pump internal check valves seat properly, a strainer on the pump suction can be used to keep rust, scale, trash out of the pump. In my experience most of these check valves are closed by springs so constant back pressure should not be neccessary for closure.

The other consideration with PD injection pumps is the spillback or relief valve. Most pumps have an internal relief valve, but many companies (including mine) prefer not to trust to these and install something external. I am not sure if there is a standard on this. This valve must be a modulating device for hydraulic service- a conventional psv will fail quickly if called on to cycle with the pump (i.e. when pump capacity exceeds controlled injection flow) and start to leak through making control unreliable.

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