Now we have a free open-source implementation of the .NET core: CoreCLR. It supports Windows and Linux operation system, Mac OS support is planned. Is it possible to run CoreCLR on Windows XP?
I dont think so. The reason is as follows: Reference: https://docs.microsoft.com/en-us/dotnet/articles/standard/library
Windows XP does not support any .NET framewrk higher than 4.0. and .NET 4.0 based winform apps or class libraries cannot reference .NET Core 1.x class libraries.
You might have better luck recompiling .NET core SDK, core clr & Corefx from sources for windows XP or any other operating system but I reckon its going to be very hard. If it were easier, MSFT would have done it in the first place.
About .NET CORE 2.0? Reference: https://github.com/dotnet/core/blob/master/roadmap.md#technology-roadmaps