Relationship between valve opening degree and flow, pressure, and velocity

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I majored in mechanical engineering; I’m working on the oil supply system for centrifugal compressors. There are some valve pressure issues that I’ve been thinking about for a long time without finding any solution. I guess I didn’t master the fluid dynamics well; I’m seeking advice from everyone here. 1. As the valve opening increases, the work required to operate the valve decreases; in other words, the pressure drop across the valve reduces. If the pressure before the valve remains unchanged, both the flow rate and pressure after the valve will increase. 2. As the valve opening increases, the flow rate increases as well, and the velocity of the fluid rises; the static pressure of the oil is then converted into dynamic pressure. The drop in static pressure (lower pressure where the flow velocity is high) is derived from Bernoulli’s equation for fluids. 3. The two conclusions are opposite; the first point is definitely correct. I have two ideas regarding the mistake about the second point. The first case is that before and after the valve opening increases, they represent two separate systems, and the Bernoulli equation cannot be applied. The Bernoulli equation holds only when considering the conditions before and after the valve at the same time; when the flow rates are the same and the cross-sectional area remains constant, the flow velocity is also the same, so the dynamic pressure is identical. However, the static pressure decreases due to losses across the valve. The second idea is that the Bernoulli equation can be applied before and after a change in the valve opening degree. When the valve is opened wider, the flow rate increases, the velocity increases, and the pressure decreases. However, at the same time, as the valve opens wider, the pressure loss decreases, causing the pressure to rise. Between these increases and decreases, it is the increase in pressure that plays a decisive role (I don’t know the exact formula, but I guess the pressure decrease caused by the increased velocity is similar to a higher-order infinitesimal of the pressure loss; therefore, it is the pressure loss that determines whether the pressure rises or falls, with the end result being an increase in pressure). 4. The pressure at the pump outlet is determined by the system resistance. If the shut-off valve at the pump outlet is closed tighter, the pressure at the pump outlet will rise, but at the same time, the energy required to overcome the resistance of the valve also increases. So, how does the pressure behind the valve change? I’m speaking incoherently; please offer your guidance.