Definitely yes. But very slowly.
Additional answer
One side is heavier than the other and is pulled by gravity to always face the Earth.
rotationis one complete spin on earths axis!!!
Its axis.
Yes. When we're talking about the Earth, 'spin' and 'rotate' are the same thing.
orbit of the moon
It takes one month for the moon to spin on it's axis.
Yes, but it is called "axis".
no and yes
one rotation is one day.
That's "rotation".
They both spin on an axis.
No. Each of those "days" of which the question speaks is the length of time it takes for the earth to spin on its axis. The question is actually referring to the moon, which takes 27.32 days to spin once on its axis.
No. It's much slower. The Earth takes a day to spin round. The Moon takes a month.