IIRC Gravity is the pull of one body on another, it isn't related to the spin of the body. We will have gravity if the earth stops spinning.

Also, we MAY have one side light and one side dark all the time, but in this case it would be a case of the earth still rotating, but the rotation would take 365 days.

If the earth completely stopped spinning, we would have day time become 6 months long, and night being the same length.

The OGRE