1. Is there a Saxon .Net XSLT Processor (that does not use the Java Runtime for processing) that we can use.
Saxon on .NET is built as native .NET assemblies (DLLs) with no dependencies on any external Java code. No Java VM is needed. However, the DLLs that come with the product do include a lot of code derived (by cross-compilation) from the OpenJDK Java library.
2. Are there different 32 bit and 64 bit Saxon .Net versions available
No, there is a single version for all platforms.