1. You know the application, you tell us. But a general-use product
needs to not place unreasonable demands or extra components.
Zero is a nice round number.
2. Resistor feedback ladder ought to ensure that there is a load,
even if no external explicit load. But it may be high.
3. If you are getting the right answer for VOUT then there is
indeed gain, maybe the calculation / method is bad. AC
analysis can give you crappy results for gain / phase when
the pass FET is buried either full-on or full-off.
4. No, the opposite. But it's not like you have much of a choice,
size derives from dropout voltage @ max load @ worst corner.