What I have seen until now:

kills

even affects Nightmare Mode (Igor remains slightly slower... Seems to be a standard effect of the boots)

kills

(yes, true)

and

don't affect each other. Getting those two items at the same time is
very crazy (Jump, then drop a bomb and kick it upwards... One of the two bombs nearly vanishes^^), but possible.
And

kills

-.- also had that some time ago...