In response to the title (and not getting into any specifics regarding your example questions), the answer is yes, questions need to be answerable. This is covered in the FAQ, and is the same for all sites in the Stack Exchange network:
You should only ask practical, answerable questions based on actual problems that you face.
It's worth pointing out that this section of the FAQ is the same for all sites in the Stack Exchange network. We've found through trial and error that questions that are not answerable are just not a good fit for focused Q&A sites. Instead, they tend to devolve into extended discussion, argument, polls, etc.
The fact that this is universal for all Stack Exchange sites explains why I might quibble a bit with the wording of "actual problems that you face". But that doesn't take away from the fact that questions need to be answerable in order to be asked on a Q&A site. If they're not answerable, they're not a good fit here. This site is very different from a traditional forum. There are a whole lot of advantages to our difference, but if you like or are more accustomed to that style, you are definitely going to encounter some friction. Reading the rest of the linked section of the FAQ should help to clarify the types of questions that we'd like to avoid.
That said, questions where the answer is "there is no answer and could never be and here's why" are perfectly acceptable. Those undoubtedly fit my definition of "answerable". For example, on Stack Overflow, people occasionally ask questions where the correct/best answer turns out to be "that is not possible" or some variation on that theme (such as, "that's the wrong way to do it; do it like this instead"). I would not close a question for this reason, and I doubt that any other moderator would, either.
Certainly the discussion about whether or not there could be an answer to a question is interesting. There are lots of questions like that in philosophy, and I can imagine all of those being perfectly on-topic here.
Getting down to your specific examples, though, the problem seems to be contained within your own explanation:
The first one has lived on and generated quite a number of interesting answers and side discussions.
Interesting answers are good; side discussions are not. We actively try to avoid questions that are more likely to devolve into a bunch of side discussions than they are definitive, comprehensive, and useful answers. As explained above, this is not a discussion site and trying to force discussion just doesn't work very well. Don't let the "comment" feature fool you: that's intended primarily to allow quick clarification of either a question or an answer. They're not intended for extended discussion. Useful discussions should be moved into a new question and posted as a new answer. Other types of discussions that can't or wouldn't make sense to post as a new question should be altogether discouraged. Please be mindful of this in the future; your experience here will be a lot smoother and, dare I say, a lot more fun.
As far as the question that was closed, I suspect the moderator who closed it hasn't seen your latest revisions. In situations like this where you've considerably revamped a closed question in response to suggestions from community members, it's useful to flag the question for moderator attention and ask for it to be re-evaluated and possibly re-opened. That ensures that one of us will see it and your hard work.
Thus, since you have put a lot of work into trying to reformulate and better explain your question, I'm tentatively voting to re-open it. I think it's acceptable as it stands, and I agree that there is probably an answer, even if the answer is as simple as "no, and here's why that's impossible".
But I do mean tentatively. If the answers start to devolve into extended "mini-discussions" of their own, or otherwise begin to lose a clear focus from the original question, I will close it again. You're bordering on the edge of the types of questions that are a good fit for this site (notice I'm talking about types of questions, not subject areas). Please keep the above points in mind for future questions.
And in closing: I'm sorry you feel like you've had a bad experience. In the future, posting here on Meta is a perfectly acceptable thing to do. And please don't feel obligated to accept my answer just because I'm also a moderator. Everyone in the community has access to the Meta site and can post answers of their own. It's perfectly OK that they disagree with one or more of us moderators. We're just trying to represent the community as best we can, through our experience and the collective experience of other Stack Exchange sites. If the community thinks we're doing something wrong, we'll be happy to reconsider, and that's precisely what Meta is designed for. (It is much more laid-back stylistically than the main site.)