That's not necessarily true if something is messing with your insulin production or sensitivity to it.
I think.
This is true. But there's no evidence (yet anyway) of diet cola messing with insulin production or sensitivity (or none that I have come across anyway). I wouldn't rule out the possibility cause you never know with these things, but I doubt it's the cause at this point in time.
The surest way to spike insulin is large amount of oral glucose intake...which is not found in sweeteners as far as I know.