You obviously know already that nearly all your questions get a flat "no", so I'll just explain why.
UNIX runs on many systems that are completely incompatible with each other. HP-UX runs on Itanium and PA-RISC... Solaris runs on x86 and Sparc... AIX runs on POWER or System/370... IRIX runs on MIPS. And so forth. They are physically incompatible with each other. Not even linux-SPARC is compatible with linux-x86, their CPU's do not have a common instruction set. They
cannot run the same binary programs, computers simply do not work that way.
UNIX can share programs which
aren't native instructions, though. Most importantly, C programs. These are the ones which actually become binary programs... You can compile the same C code into binary programs for IRIX, HP-UX, AIX, or Solaris. This is what lets UNIX run the same program on umpteen different kinds of completely alien computers. This is what all these different UNIX have in common, they call it "source compatibility".
If UNIX had to be "compatible" the way you want, it would run on one and only one kind of computer -- the
PDP-7.