I've seen that come with Rule
pumps say no check valve. Other companies say it's ok. One of the problems is that the weight of the water on the check valve can keep the pump from pumping if there is air in the pump. Centrifugal pumps don't pump an air water mix well, so it might not overcome the head
and the air can't escape up the hose. My theory why some companies say that it is ok to use check valves is that the design of the pump somehow allows the air out or can never trap it in the first place.
Here's someone with 4 reasons:
Resist Using Check Valves
What has become recommended is to mount a small pump with a small hose in the lowest part of the bilge
to make the bilge as dry as possible, and mount your bigger pump up higher for a more serious leak.
As the other poster said, no anti-siphon needed unless your outlet can go underwater. The recommendation in your Rule manual is if the outlet comes within 12" of the waterline worst case, i.e. heeled over, then you need the loop.
Just has pictures but your manual had all this information in it. You should have one of these with your pump: