I would go for high gloss mustard green wet wall where the tiles were. This colour looks great with aubergine and the sleek finish will instantly update the kitchen. Positional ceiling halogens and lighting under the wall cupboards to make the rich colours glow. I think three colours are fine, especially if you pull them together in a blind fabric or cushion. ???

I must admit I am scratching my head a bit on this one - the two slightly different shades of cream don't make it easy! If everything wasn't split new, I think I would be recommending changing the tiles. I'm not a fan of painting tiles either, but I am really at a loss as to what to suggest. A teal perhaps or verdigris, but I think whatever colour you pick, the tile/cabinet combination may still feel a little unbalanced. Might be worth thinking what you can do to mask the tiles with nicely coloured appliances, possibly an accessory rail, fruit bowl, plants/herbs etc.

What colour is the wooden floor? And what colour have you,chosen for,ceilings and walls?

It sounds like you have plenty of natural light coming in so should be fine with most things. I think the blue all over would be a little too much with north light - making it feel a little cool. I would go with the suggested half and half which will also lift the height a making it feel more open. With the blue itself I would try to go for something with as warm an undertone as possible.. same with any whites you choose. If they have blue or grey undertones they will feel a look more drab with the specific light that's hitting them. It sounds like you're going to have a fab space! :)