1. I have no response to question 1.
2.a.
How does stiffness affect the calculation?

The result is typically both conservative and non-conservative, depending on your pipe routing, support layout, and estimated versus real world stiffnesses.

What do I mean by "both?" Imagine you have an anchor, "short" pipe, a bend, "short" pipe, and anchor. On both "pipe" elements, you place 0" gap guides of standard flexibility, and anchors of standard flexibility.

Because your pipe is quasi-infinitely flexible compared to the supports, your simulation shows the elbow collapsing more than reality.

Because your supports are quasi-infinitely rigid compared to the pipe, loads on guides and anchors will be higher than reality.

However, because your guides are infinitely rigid, they act as a mechanical fulcrum, and instead of a load in the positive direction, it shows load in the negative direction. It may be higher in magnitude. It may be lower in magnitude. Given enough iterations, you might even find a case where the location of the guide can fictitiously zero out the load in a given direction.

2.b.
How do I arrive at stiffness value F=kx?

If you modeled an anchored pipe and applied a load, F, laterally, to the end, it will displace x. You just calculated the spring factor for pipe.

A structural member isn't very different from pipe, in that way.

3. Lateral loads, whether from earthquake or wind, will result in large scale deflection in long, unguided pipe. In the absence of guides, friction will have a dampening effect on how far the large scale deflection will be, but CAESAR will easily outpace what you want your pipe to travel (and run into other things, fall off supports, fail, etc).