You can try cleaning the grout with bleach as suggested.
If that does not work DIY places sell small scraper to remove old grout, This is not too easy and takes time.
Clean surface with bleach then re grout.
Silicone - again first try cleaning with bleach,
If this does not work taking great care not to damage surfaces use flat blade and cut away old silicone. Again you can buy silicone remover from plumbers merchant. Make sure surfaces are clean and dry and renew silicone bead.
As suggested your problem is due to lack of heat and or ventilation, Might be worth looking to get an extractor fan fitted in window or wall. Might cost a bit buts its more fun than cleaning walls!!!
Maurice, February 2011