If the silicone is black the only thing I have found to rectify this is to replace the silicone. When you replace it go for the good stuff, this is really one of thoes situations where if you buy cheap you will buy twice and it is total PITA to scrape out the old silicone. To scrape it out i have found the window scrapers you get with stanley blades in them to work well.
To prevent the mould coming back better ventilation is required, but what i have also found to help is a quick wipe down of the screen and tiles with a window squeegee to get the worst of the water off the walls.
For grout i have had sucess with asda 19p bleach and an old tooth brush and scouring pad. Thin bleach works fine and as long as it is not coloured it should do the trick.