I think it's important to understand definitions here (it looks like you mostly do, this is just to make sure).
First, assembly language: that's simply any human-readable language where each statement is compiled directly to an instruction in some machine code (which could be for example x86 machine code or .Net bytecode).
Based on this, disassembler is a program that reverses that compilation: it converts machine code to the corresponding assembly language.
And decompiler converts machine code to another language.
Maybe an image of all the options (including de-/compiling C/C++ and assuming x86 computer) would help:
Now, to your specific questions:
Is it possible to see the assembly code (from the Dissassembly window) generated by the Jitter in a text file?
Theoretically, there is no reason why that shouldn't be possible (especially considering NGEN). Practically, I don't know about any such tool.
Is MSIL an assembly language or a high level language in the context of my first question?
I would say that it's a high-level assembly language. It's certainly an assembly language and it's also higher-level than normal assembly languages.