First off, there is a part missing in your Lovejoy coupling. The part is called the coupling insert, or "spider". It's a polymer cushion so you don't have metal on metal contact like you have. You can see your coupling fingers are destroying themselves (circled in red in the below pic). You should replace the entire coupling assembly, but merely installing a new insert will get you by for awhile.
View attachment 1164444
If you scroll down to the second parts diagram
here, you'll see it called out as #10 on the diagram. Most farm stores carry them.
The coupling should look like this. You can see where the coupling fingers are isolated from each other and cushioned by the insert.
View attachment 1164445
I see the key for the engine side is there, but did you verify the woodruff key on the pump side isn't sheared? You cannot see it without removing the coupling half. It will be under the set screw on the pump shaft. The woodruff key is called out on the same parts diagram as above as #35.
As far as how the control valve is mounted, it appears it is held in place by being threaded on the rigid pipe that goes from the control valve to the cylinder trunion. I don't see a bracket anywhere.