Re: Cleaning grout
Coincidentally this is a task I am doing at the moment. Aren't we lucky?
I've got a specialist grout cleaner from Homebase (other DIY chains are available) - it's a nasty caustic sort of thing but it works pretty well, though it needs elbow grease
I think it's grease which is the main problem with the cleaning, so perhaps even a solution of 'washing soda' would be a good degreaser before you tried with a detergent-type
I've heard people praise Cillit-Bang but I think it's a bit fierce and likely to dissolve your tiles!!!
Whatever you try best to do a test patch somewhere non-vital first
Good luck - let me know if you find a miracle product