Is there an SE site for asking for a complete and working program example, given an arbitrary set of conditions? (Like OS, compiler, what the program should accomplish, and what not.)
I am pretty sure this is not best place to ask, but it's definitely meta... and I could not think of any better place.
No, there is not such an site in the SE network and I doubt there will ever be one.
What you describes sounds more as a build to order request which is more suited for sites that match demand and supply against a fair price, not for sites that have content created and curated by volunteers.
The other issue these kind of questions have is the highly specialized and small applicability for just a single person, namely the OP. That is not what the SE network strives for. They want questions and answers that are useful for future visitors. You will find that guideline in a couple of sites where questions that are only for benefit or advice for the asker are discouraged.
The closest sites that offer finding an answer for a given strict specification are the two recommendation sites, for Software and Hardware. They both link from their help to strict quality guidelines posts on their meta.
The best you can get is implementing the program yourself in a language of choice and ask a specific question about a specific practical issue you run into, given it is not asked before. Those type of questions could fit on Stack Overflow, and design aspects might work on Software Engineering.
In general, you can end up with a program that consists of answers from many questions, not with a program that is the result of one question.
