Should we consider Cygwin on-topic here? It's similar to a Linux command-line and has many of the same tools, so lots of answers will probably just be the same as if the user was on Linux. However, it also has quirks and oddities that are cygwin-specific; there was an SO post recently that wouldn't have happened on a normal Linux install
Certainly just because you're using the Cygwin version of vi or bash doesn't make a question about regexp replacement or brace expansion off-topic.
When it comes to questions that are more directly tied to a particular implementation, it seems to me that since we allow questions about interactions between Unix implementations and hardware, we should also allow questions about interactions between Unix implementations such as Cygwin, GNUWin32, Windows Subsystem for Linux (Ubuntu on Windows, Bash on Windows), coLinux, etc. and the underlying platform.
However, if a question is essentially on the Windows side and the fact that Cygwin is a Unix implementation is completely incidental (e.g.
cygwin1.dll woes), I think it should be asked on a Windows site, because I don't expect that there is much expertise about Windows on this site.
Cygwin is a POSIX compatibility layer (and a little more, and a little less) on Windows. So it is *nix sort-of friendly. Therefore I would consider it on topic, with the provisions that Gilles makes.
I would say in the general case no, but the Pee-Wee Herman rule applies.
If the asker appears smart and groks UNIX conventions and asks "the right way" it can be OK in some circumstances, as they would be an asset to the community.
I assume Cygwin is not Linux, but I assume it's Unix (or at least Not Unix (tm)).