1-- it's idiomatic, but I suppose it means something like what you said:
this time, then nothing, then that time. Yes, they are essentially synonymous:
from time to time; sometimes; occasionally; now and then, etc.
2-- The apocryphal origin is in the businessman who was suddenly asked to give a speech, and wrote a few notes quickly on the cuff of his shirt, to which he could refer if necessary. Hence the speech was presented '
off the cuff'.