Your first question finds an answer in this Wikipedia article :
if the fluid flow is irrotational, the total pressure on every
streamline is the same and Bernoulli's principle can be summarized as
"total pressure is constant everywhere in the fluid flow". It is
reasonable to assume that irrotational flow exists in any situation
where a large body of fluid is flowing past a solid body. Examples are
aircraft in flight, and ships moving in open bodies of water
And for your second question, I would say that the effect of the height difference is negligible compared to the velocity and pressure terms.