I have a tile roof, plus some cracked tiles
First you want to fix the cracked tiles have a qualified roofing contractor that works on tile roofs replace the cracked tiles, Most moss, leaves,bird dung ect… will come off with a medium pressure washing
done from the top down have a professional do this ,It can be pretty dangerous attempting to do it your self most contractors will bring a boom lift to be able to reach most areas of the roof to clean, some chemicals or harsh detergents can harm different building materials on your home ,ask a pro they can recommend the best product suitable for the job.and the best methods.