Ceiling crack
Cause
Hairline ceiling cracks are normally caused by differential movement due to temperature & relative humidity, and nothing practical can be done to stop them. Attempts to prevent future cracking don't work. Sometimes people cause damage trying to stop future movement.
Fix
When hairline cracks occur, just wipe the crack with a finger with a bit of filler on. Wipe any filler off the surface and its done.
Occasionally the 2 sides of the crack move up & down relative to each other, and wiped in filler soon falls out. If this happens the 2 plasterboard edges need to be connected to each other so neither can flap. Lift a floorboard above, place wood strips above the ceiling and screw through the plasterboard into them. Only use plasterboard screws, other types break up the plasterboard.
Another fix for flexing edges is to drop large globs of plaster onto the ceiling from above to stick it together. This works well with lath & plaster ceilings, using a lime mix.
Don't
Often people gouge the crack out before filling in the mistaken belief that this is likely to prevent future cracking. It doesn't, it just worsens the damage. Worse they often overfill it then discover once set that they're not going to get a decent result by sanding it down.
Fix damage
Where damage has been done by gouging the ceiling & filling badly, the solution is to fill/level the damage. Do it well & its invisible. Some folk apply excess filler & sand it down, its much easier IME to level the filler when its applied, not sand it later. If cracking is extensive it can be easier to skim the whole ceiling.
Flexible fillers are ineffective since they have only slight flexibility, and the amount of flex required to continue to fill a hairline crack is 100s of %.
Edge cracking
Small cracks are best filled the same way, just wipe on some filler.
Substantial cracking at the ceiling perimeter can be reduced by fitting coving or cornice, fixing it only to the wall. Cracking is still visible, but less.