seems like the vinyl is glued to the bathroom floor. How can I tell for
certain?
Only 3 square inches of the bathroom changes color.
How do I remove & replace the entire bathroom vinyl, many be with ceramic
tile?


Don't rip up the subfloor just the underlayment above it. Its usually 1/4"
particle board. You need to verify what you have underneath before you
adjust you circular saw for a 1/4" deep cut and let her rip.

I think you're screwed (very time consuming to remove that is) if its
glued
directly to the subfloor.

I also have a small corner by the bathtub that needed to be repaired but I
try to remove just that portion of the vinyl and damaged wood and patch it
up with a matching section. May end up ripping the whole bathroom floor or
lay another floor (laminate) over the existing vinyl, but I'll try to save
it first.