I have a 1 HP. So if I am reading this chart correctly it is says that at around 400 feet where my pump is it is producing about 4 GPM running around 60 PSI? Being that my shut off is set to about 65 psi and draw is set to 30psi on my switch. Within that range I'm pumping out 4 gpm. Correct?
Not quite. That would only apply when you are about ready to run out of water. Suppose your system is set to 40 to 60 for easy calculations. Suppose the static water level is 300 ft. Then ideally, at 50 PSI, your irrigation system would draw about 6.0 GPM. The pump would not cycle. If you were drawing a little more, the PSI would drop. What if you flushed a toilet in the house? The pressure would drop some. If the total draw went to 7 GPM, the water pressure could drop to 20 PSI. But the total GPM would probably not rise that much, because as the pressure started dropping, the sprinkler heads would start drawing less water.
There are graphs that let you figure out the flow for whatever conditions. They are not as easy to use as the tables, but they are more flexible. Alternatively, if you wanted the GPM at some other pressure, you could adjust the depth to water to get an equivalent. A 5 PSI pressure difference at the surface is the same as changing the depth to water by 11.53 ft.
Is that adequate to run my system without a booster pump?
It could be. It depends on the irrigation system... If you do use a booster pump, 2 HP seems very oversized. You could use a CSV on that booster output as a regulator, it seems to me. Then the sprinkler heads will see less variation of pressure.
I certainly would be looking to get rid of that check valve to the house. And if you keep that check valve, it seems to me that you would want a pressure tank after the check valve. But no check valve to the house seems best to me.