Left handed neck on a right oriented bass?

You would need to modify the nut, sometimes popping it out and reversing it works, other times replacement may be necessary. Some string sets may not have sufficient winding lengths on the E string.

 

Yes it is just as simple as flipping the nut.

 

All of the above.
Being a lefty, and having flipped righties, I would suggest a new nut and some nut filing rather than flipping it.
The nut will be shaped to a lefty neck, so when you flip it, it will have a sharp hard edge on the exposed side. It can often break strings.
Also, you won't have side dots along the neck, and the string length can also be an issue, but not much..