Flanders is not a city ;-) It's one of the 4 regions of Belgium... one is dutch speaking (Flanders), one is french speaking (Wallonia), one is Brussels and its surroundings where we are supposed to be able to speak both languages (in theory) and the last one is german speaking. But I guess this doesn't change anything for Homer :-D
I think emphasazing this as a mistake is artificial. The name "Holland" is commonly used and in some countries used interchangeably. It's just like we say USA instead United States, Great Britain insted United Kingdom etc. Switzerland is also a name of an idividual region but we don't say Confederation of Helvetia...
I don't know if "staat" can always replace "is", but I think that "staat" is the third person singular form and "zijn" is the third person plural form. I am pretty sure that you can replace "staat" with "is", but "staat" implies that someone is "standing" and we don't know if they are sleeping, or sitting or standing. If we did know that they are up, than "Zij staan in Nederland." would be the way to say it.
Usually, the Netherlands.
Other than that this is a Dutch course and for that reason the decision was made to only allow the Netherlands to make clear that Holland technically is only a part of the country. Think of it as similar to saying to someone from Scotland or Wales that they live in England.
Even though in English English Holland and The Netherlands are synonymous you will get a barrage of people pointing out that Holland is just a part of The Netherlands as a whole. Which is quite correct. It is also true that in the UK if a person says Holland they mean The Netherlands. Yes I tried the system by putting Holland once, just to see what happened. I discovered!