regarding grout I am a grey grey on floors and white on the walls man, one brand of adhesive i used in the UK had 32 colours of grout with matching colours of silicone,
just use some bleach on the grout should clean it,
yes the gap should be about 3mm to allow for expansion, should also allow a gap around the outer edge of the tiled area, also you should have an expansion gap every 8metres of run, that's where the matching silicone colours come in,
laying tiles with no gap is asking for trouble, the same thing goes for not using a suitable thin bed adhesive, especially for porcelain tiles