1.
An N-mosfet has its gate referenced to the source terminal. In order to turn on, the gate voltage needs to be higher than the source terminal. The source terminal should have a definite path to ground, for proper operation.
However your upper two mosfets appear not to have this at times when the lower two mosfets have shut off.
Do you have a load connected? Try a resistive load at first, and it should provide a path for the gates to have a definite reference, both to turn on and to turn off.
2.
Although your schematics show no zero ground, this is probably corrected in your real circuit, because you say you got it working to some degree.