Will some expert please please enlighten me. Thanking you profusely in anticipation.
I'm not an expert, but here goes:
1)   It is my understanding that if a control valve is installed downstream of a centrifugal pump, then the following will occur for minimum flow:
namely, the ACTUAL inlet pressure will be maximum and the ACTUAL pressure drop across the control valve will be maximum.

Similarily, the following would be true at maximum flow:
namely, the ACTUAL inlet pressure will be minimum and the ACTUAL pressure drop across the control valve will be minimum.

This is true when the control valve is the only thing that is used to vary flow (no other flow-regulating devices in the loop).  Also your comments about inlet pressure are a little vague... depends on where the static pressure is being controlled (expansion tank on pump suction?)

In other words, for increasing load (flow), the ACTUAL pressure drop across the valve is decreasing.
yup.
Question A:
Are the statements in (1) above correct?
yep.
Question B:
Will someone please explain to me why, in some situations,
the pressure drop across a control valve would INCREASE with INCREASING load?? What are these situations?
If there are other devices in the loop controlling flow, this can well be the case.  For example let's say we have one control valve on outlet of a pump, and then many individual flow-control valves on heat exchangers loads (in parallel with each other off of the header).  Let's say it's a cooling loop and cooling water temperature goes up. Then all of the individual loads start heating up and the individual valves start opening (through automatic or manual action based on temperature of individual loads). Then the main control valve would see increased total flow and start closing. In this case total flow may be increasing while control valve is closing and it's dp is increasing.  As an approximation, consider the dp accross the pump to be constant. This dp will divide among the control valve and the equivalent load comprised of all the individual throttle valves. In the scenario above the flow resistance of the main control valve went up and flow resistance of the individual throttle valves went down. The main control valve will assume a higher fraction of the total dp.

Question C:
When a process engineer fills in my valve spec sheet with the MAX deltaP occurring at MAX flow and the MIN deltaP occurring at MIN flow, how do I determine if this is the actual case or if indeed this is not correct and in actual fact the MAX deltaP occurs at MIN flow and the MIN deltaP occurring at MAX flow ????
ask him?