"Number of times this creature has mutated" only counts for while the creature is on the field, and not throughout the game, right?
"This creature" only looks at this creature, not at any other creature that might have been on the battlefield in the past, even with the same name (or very similar cards).
403.4. Whenever a permanent enters the battlefield, it becomes a new object and has no relationship to any previous permanent represented by the same card, except for the cases listed in rule 400.7. (This is also true for any objects entering any zone.)
The "number of times [a creature] has mutated" is the number of events in which a mutating creature spell merges with that creature (see also C.R. 702.139c-d). It's not necessarily the number of cards and tokens that make up that permanent minus one. For example, if a mutating creature spell merges with Chittering Host, a melded permanent made up of two cards that hasn't "mutated" yet, the resulting permanent has "mutated" only once, not twice, even if the permanent has more than two components. See also this thread.
Like the number of creatures on the mutate stack is the number that applies to that mechanic?
Just making sure.
"This creature" only looks at this creature, not at any other creature that might have been on the battlefield in the past, even with the same name (or very similar cards).
For example, if the merged permanent has 5 components, its history includes 4 mutates.
EDIT (Feb. 16; Jul. 21): Correctness edit.