Hi
I have seen your other posts on the subject and replied in one of them. But have you made any attempt to understand the differences between linear and non-linear buckling beside posts in this forum and the youtube-link you had in another tread.

Regarding your questions. In non-linear analysis the stiffness can be stress dependent. It can change due to cracking in concrete or due to yielding in steel. In linear analysis it is a constant.

Regarding geometry, again, no a simple question. It depends om what effect the deformations will have on the structure. For a wire, increasing the stress means higher stiffness and decreasing means the opposite.

I can't help but wondering, are you a student?

Thomas

Consider the simple example of a beam-column. If you were to ignore lateral deflection of the beam (due to transverse loads), you would have an unrealistically high column allowable.
I think this analogy answers your question.

You should start from learning about geometric nonlinearities themselves. There’s a nice example of a clothes line subjected to point load on Enterfea blog (in one of your previous posts you’ve already referenced a lecture by this blog’s owner Lukasz Skotny). However, you can also study the behavior of cables in general.