Ans: 1 - For me it doesn't, this surprises me a little, but I can move from one scale length e.g 35" or 34" scale bass to a 30" SS without issue. There are differences with string tension and spacing that I occasionally get caught out on, but depending on what I'm playing, within ten minutes, it is a non-issue.
Ans: 2 - I don't experience neck dive on any of my short scale basses.
Qu: Which SS bass that you've played presents neck dive issues?
Ah, just read through a few contributions to this and yes, Fender Mustang variants have some neck dive, I hated the one that I played and I don't own one.