Carpets would be the preferred choice over tiles.

The chairs are a good match. Leather is probably best, great for kids' spills and accidents, but any fabric will do. Not sure on purple with green - those two colours together clash a bit for me. The green kitchen looks great, and I'm a fan of dark wood. The only thing throwing it off at the moment is the yellowish coloured walls. If they were repainted a soft white, this would make the green and the dark wood really pop, giving you a fresh and sophisticated, calm look which I think would work well. You could then upholster in a green to match the kitchen which would look appealing. Finish it off by some fresh white flowers as accents in the room to draw the eye and you've got a beautifully transformed space with a fabulous feature dining area :)

squeakerd - it is really hard to get a perspective on the whole area but if this is part of a much larger area then I feel you need to first decide just what you want as the end result. Do you just want your entire area to be one open plan or do you want to break it down into visually defined areas within the open plan. As you have the area now, I don't feel any cohesiveness between your table and the sideboard, I think I would move the sideboard to the end wall, it looks more like it would belong there, even just by the shape of the room. Definitely a larger rug will define the space better - just be careful of any trip hazard with the door nearby - but before you decide on the rug, consider window dressings and whether you want things plain or introduce some bold patterns and what colours look best in the area. Artwork can go where your sideboard is now, but again think colours and impact of design on the whole area. It is all very well to build a room around one piece, but you need to look at the impact that piece will have on other items and what limitations it could cause. I would suggest you set aside some serious time to look through photos on Houzz, especially if you can find areas similar to yours, till you find what appeals to you, put the photos into your ideas book and use that to build your room. I have found this invaluable in the past and it has saved me many an expensive mistake.

I would wait for the rug, until you have the shutters up and your furniture placed..it may take on a character of its own and you'll want to compliment. My first thought though was to coordinate with your kitchen and incorporate some black, with a black/beige stripped rug, which would be fun with the wallpaper and perhaps paint your chairs black, add the shutters and you could paint the window trim black and add a large black chandelier.