What happens if gravity shuts down for only one second? What would happen if gravity completely stopped for 1 second?
I expect stars would belch mightily, neutron stars and black holes would explode.

Stars are only held at their steady state size by the opposed forces of gravity and radiation, so eliminating gravity for 1 second will cause expansion, followed by collapse as gravity kicks in again.
A Neutron star's compactness gives it a surface gravity of up to 7×10^12 m/s², and expanding from 20km to ~70 billion km (or 300000km when c limit is considered) over the course of 1 second constitutes an explosion.
Black holes tend to have higher gravity values at the event horizon (same ref) so the result would be even more cataclysmic.