You can `dotnet publish MyApp.fsproj` on either Windows or Linux, copy the resulting `publish/` folder to another machine with a different OS, and use `dotnet MyApp.dll` to run it. There are also ways to create containers, though I have never tried them for lack of an actual use case.
As for libraries, .NET comes with a huge standard library, much larger than what you would find on a different language. Off the top of my head, here are a few things that come with .NET that would have been a third party library in other languages: text encodings, protocols (HTTP client, TLS, QUIC, SMTP), mainstream hashes (MD5/SHA1/SHA256), mainstream crypto (AES/DES/RSA/EC/ChaCha), serialization (JSON/ XML), weird formats (X509/ASN.1/tar/MIME), mainstream compression (deflate/brotli/zip), binary data manipulation (e.g. endianness conversion, AVX intrinsics, memory-mapping), runtime code generation, in-assembly resources, interoperability (COM, JavaScript, Objective C, SQL), concurrent collections, async...
Besides, since C# is popular, many tools have .NET-compatible clients or libraries which can then be accessed from F#.