Yeah I think this is the original design doc for NT.

IIRC Microsoft's internal email still ran on Xenix at the time (until Exchange betas got good enough for internal use c. 1995?), so perhaps more trademarks than some sort of absolute hatred of Unix. Also note that one of the two APIs that NT OS/2 was initially going to support was POSIX, albeit perhaps more because the US government wanted that than a true love of UNIX. Although the design rationale document (ntdesrtl) does lament that existing POSIX test suites tend to also test "...UNIX folklore that happens to be permissible under an interpretation of the POSIX spec".

It is a generic way to refer to unix and unix-like systems. It is still in use today, e.g. to indicate Linux as part of the set. For this document most likely it refers to Xenix (MS's unix).

I think trademark, I remember Bill Gates referring to Windows NT as "a better UNIX than UNIX".

Microsoft's eye wasn't on open sourcing their OS and describing the deep internals. They still don't want you to develop against the NT API, even though developers certainly do (and Microsoft makes compatibility shims for applications which do, when required).

This mostly describes stuff to do with the [Windows] NT [OS][/2] (delete as appropriate) kernel layer, which normal mere mortals aren't supposed to interact with. You're supposed to use stuff like the Win32 KERNEL32.DLL not the more direct DLL, NTDLL.DLL (a DLL). Of course, true hackers scorn such abstractions.