Okay, so now I have actually booked an Israir flight instead of an Arkia one -- because cheapoair emailed me and said the time of the Arkia flight had been changed. Since the new time didn't work, I just got them not to charge the ticket since they hadn't done so yet.

Now I see on the Israir reservation they have an unhelpful comment saying:

על אף האישור שניתן ע"י מנהל התעופה האזרחית, מועד הטיסה עשוי להשתנות או להתבטל
"Despite the approval given by the director of civil aviation, the date of the flight may change or be canceled"

Clearly this is all a bit of a mess! How can I be sure they've even ticketed this? The flight is in only a few days' time.

I can't see any ticket numbers on the Israir invoice or emails and there doesn't seem to be a six character GDS code to look up the reservation. Any idea how to find the ticket numbers?