Ceiling holes needs to be made good.
Damp areas / staining to be treated with a bleaching agent preferable and then wiped off with warm clean water.
The whole of the ceiling then needs to be washed with sugar soap before decorating.
Once ceiling dry of washing, treat with two coats of white good quality emulsion

Cut out sealant to shower tray.
Re-seal shower tray with good quality white sealant, around whole of tray against wall.