2) You will not be able to take a WIndows container and run it under Linux without a Windows VM on top of linux (which means license?), in which case it would make more sense (to me) to run it directly on Windows (cut the middleman all together).
3) Many apps, for example mysql, nodejs, and the CLR, have binaries for Linux and Windows. With these you'll be able to deploy to Linux or Windows (you'll need a matching container image of course). Choosing where to deploy will depends on many factors. I think it'll depend mainly on ( a ) maturity of the support on that platform, ( b ) what you use in your shop, and to a much lesser degree ( c ) on performance.
4) A big unknown today is the level of maturity of the CLR on Linux. And to the level of how much will Microsoft invest in it compared to WIndows. Only time will tell.
4+) If the Linux CLR (and/or mono) reaches par with windows, ms can pretty much shut down its server department ;)