For (1): I'm not sure but have you checked "Programmer Time" under the Z key? Or SETUP+BUTTON and ensure any fade times there are 0?
For (2):
Make the cue live on stage.
Select the fixture.
Press HOME.
Press and hold UPDATE.
Select REMOVE. (Also confirm cue only/track forwards setting).
Press ENTER.
See: https://www.zero88.com/manuals/zeros/cues-playbacks/updating-cues/update-options#remove
You can probably arbitrarily select the fixure (without making the cue live on stage) then when you do the UPDATE also type the cue number and at the end instead of ENTER, press the GO button for the playback containing that cue number. However I've never done this, but Edward shows that here: