What is the cause of "Static Pressure" in flowing fluids? How do we understand the idea of static pressure intuitively?

Pressure is caused by constraining a fluid*

All** pressure is the result of constraining a fluid to a container. In other words, the walls of your container provide the force that "causes" there to be pressure in a fluid. An example of a fluid flowing in a constrained space is water in a pipe that changes diameters (your item #4). An example of an unconstrained fluid is a droplet of water in free-fall, like those created by astronauts on the ISS.

An intuitive explanation of pressure:

An excellent analogy to pressure is the normal force of a block on a frictionless incline. The incline constrains the block's motion by applying a normal force. When the incline is vertical, nothing is constrained and the normal force is zero. When a container constrains a fluid's motion, it applies a pressure that is felt everywhere in that fluid. Without a container, no pressure is applied**. See the below illustration:

* Please only liquids and gases, no plasmas please :).

** we must exclude systems that violate a quasi-static equilibrium (e.g. shock waves, free expansion, etc.).