If the difference in pressure is zero between two points of a horizontal constant radius pipe, why isnt flow rate zero?

In a straight pipe of uniform cross-sectional area filled with a nonviscous, incompressible fluid, the pressure at one end is equal to the pressure at the other end. Which of the following statements is/are true?

I. The volume flow rate is zero because there is no net force on the fluid

II. The volume flow rate is constant throughout the pipe because the cross-sectional area is uniform

III. The pipe is not inclined relative to the horizontal since the pressure is constant.

My Logic:

Bernoulli’s Equation tells us: $P_1 + frac{1}{2} rho v_{1}^2 + rho gy_1 = P_2 + frac{1}{2} rho v_{2}^2 + rho gy_2$.

Knowing that $Q = vA$, the velocity is the same on both sides since the radius is constant. I also know the volume flow rate is constant (Choice II) <- What are the conditions for using this equation?

Since the pressure is the same on both sides, $P_1 = P_2$ so the pipe has to be horizontal otherwise we wouldnt have conservation of energy. (Choice III).

I assumed that since $Q = frac{dP}{R}$ that the flow rate would be zero but I’m told that isn’t true. Why isn’t it?

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Part of my question is when these relationships apply:

Bernoulli’s I can use when i have incompressible non viscous fluid.

$Q=vA$ (same requirements as Bernoulli?)

$Q= frac{dP}{R}$ (?)