Interesting questions. I'll try to give you some thoughts from my side.
For some background: I run a tech company in Austria, Europe. Austria is not the US, but more or less comparable from an income perspective. Culturally it is very different though (definitely not as entrepreneurial as the US).
Not sure. I think entrepreneurs are generally driven by the will to make something big. If you're just looking to survive you could easily stop at some point, but most entrepreneurs never really stop.
Moreover, I would argue that the pressure to survive is higher in lower income countries than in higher income countries. For instance: in Austria the pressure to survive is rather low, because of the social welfare state we have here (that may be very different in the US though).
I have not made this experience. Especially in the US people seem to be very result driven. So, they care more about HOW to achieve a result not about WHO can achieve a result.
The most successful companies I know are NOT looking for cheaper ways, but for better ways to achieve something.
Generally I tend to agree, but there may be a counter argument that people tend to get lazy if they have everything. I guess that's why a lot of successful entrepreneurs are in the sweetspot of not having a big financial heritage but they still had the luxury of growing up with choices and a "good" education.
That's a problem for sure. But even beyond that: Maybe a reason why so many new things come from the Valley (or richer countries) is, because you get to experience new technology very early. i.e: How can one dream of creating a video streaming service if you're still on an unreliable 56Kbit connection...
I think that one is very SF specific. Outside of the Valley this seems to be true for almost any place that I travelled to.
I don't think this plays a role. You can always put up a website or an App and start marketing it to US customers or anyone in the world.
All entrepreneurs that I know dream big. I don't think this is something specific to income or origin, but this is just my experience.