Mouldy and cracked bathroom ceiling

Hello, I need to renovate a mouldy bathroom. There is mould in the ceiling and also a crack in it. Can I get rid of the mould and repair the crack and if so how (I know nothing about practical do it yourself work) ?
Alternatively do I need to replace the underlying plasterboard? If so is there an anti-mould ceiling plasterboard I can buy? I also need to replace the bathroom fan which is ineffective. Can anyone recommend a very strong bathroom fan please?