The elongational or axial stiffness (elasticity has other meanings in similar context and should be avoided here) of a string (or anything else) is defined as the force required to cause a given displacement, i.e., stiffness = Force / displacement.

This can be related to more convenient parameters by writing it as:
stiffness = elastic modulus * cross-section area / length.

Elastic modulus is an inherent property of a material and won't change (unless there are nuclear reactions occurring within your guitar strings which change the chemical elements). Presumably the cross-section of the string is constant as well, though it does change very slightly as the string is stretched (which also means the length is changing). This leaves only the length of the string available to change.

I have never heard of this problem and can't find anything like it online; I suspect it is impossible to accurately diagnose with only the given information, but my guess is that some part of your guitar is loose. I would start by checking that the bridge is properly glued down, then check the nut and tuning pegs are tight. It seems unlikely, but you could also check the truss rod in the neck. Trying to notice whether the sound changes after moving the guitar a certain way or some playing styles (e.g., large string bends) might help to find the issue.

That sounds weird! I can't imagine. Your first sentence gave me the 2nd link. My best guess is this:

5 Signs It's Time To Change Your Guitar Strings "Your guitar strings feel stiff ... Your guitar strings should always feel flexible and bendable (unless of course you're playing extra heavy".

Frequency and Pitch "Changing Pitch. The four properties of the string that affect its frequency are length, diameter, tension, and density. When the length of a string is changed, it will vibrate with a different frequency. Shorter strings have higher frequency and therefore higher pitch.