I take major issue with points 3-5.

Point 3: Water is always strives to be "level". Water always strives to be in the lowest energy state. It will attempt to find equilibrium with all forces acting upon it. Generally, the only force significant enough is gravity, which acts consistently across the entire surface of the water, causing a generally level surface (level as in the same altitude, which would mean a curve across sufficiently large bodies, see Point 4 below). However, on smaller scales, forces like air pressure, surface tension, and even magnetism, can override this tenancy. In the example shown or a container with 4 different openings, unless the container is massive, each of the openings would posses a meniscus. When is free fall, water tends to form droplets, and ignores any kind of "level" alignment. This point is either a gross over simplification, or willful ignorance.

Point 4: Rivers flow up hill. I assume they're talking about rivers having to flow over the curvature of the earth to reach their destination. I'm having trouble understanding how they are even confused on this point, so I'll try to explain what I think they are getting wrong. Specifically, the Mississippi River is cited as having to "ascend 11 miles" to reach the Gulf of Mexico. Why is it ascending, why not descending? The problem is this argument appears to assume that gravity works along a single plane, then arbitrarily pics a plane on which it works. In this case, they appear to be assuming the gravity will be on a plane that connects the rivers head and mouth, and would be consistent across the entire journey.

The problem with this model is that no one has seriously proposed that as a description of gravity for hundreds of years. This person is either intentionally creating a strawman, or is woefully ill equipped to be trying to argue against the current theory of gravity. Anything closely resembling a modern model would state that the angle at which gravity acts on the river would be different at any particular point. The water would always be flowing down hill, because "down" is constantly changing as it moves across the surface of the earth.

Point 5: "Many rivers would be flowing up hill". This is a generalization of point 4. "Down" is very subjective, as is best defined as the direction the dominant gravity source is pulling (in this case the earth). These arguments still assume gravity is working along a plane, then define half a dozen different planes that gravity apparently works on, different for each river. Again, this isn't what is being proposed by anyone, so I don't understand why this argument is being made.