There is no specific regulation but it would not be recommended behind a gas cook top. If there is a concern you could install the timber behind a glass splash back for protection. There is also a really nice tile that looks exactly like timber as another option.

I work in tiles all day. Glass and mirrored splash backs are on the way out. Texture is what everyone is chasing now. Lots of interesting textures and tile shapes coming in particularly hand made looks in gloss and mat. Maybe 150 x 75 mat laid in a herringbone style (45 degree) or black gloss or matt laid brick or h/bone with contrasting grout. For a modern look 600 x 300 size tiles with grooves in mat finish. Bright colours with black and cream such as red are great if you like them but if you plan to sell the majority of people don't seem to like bright colours in tiles and your colours are classic at the moment.

In that case I think you can pretty much pick any tiles you love as the rest of your existing pallet is classic and neutral (white, grey, black, stainless steel, glass and timber). I'd suggest heading down to your local tile shop, grabbing some samples of what you like and then place them in each of your spaces against your existing features to see how they work, look at them at different times of day to see how they work in different lights. One of the paint apps may also be useful if you are thinking of painting too.

Great job on the kitchen and I agree with some of the former comments - a glass splash back would look good and the silver seems a good choice. If you decide to go with tiles I would suggest a White Tile with a smattering of Black and Grey markings with the colors prominent not subdued. I wouldn't think Brown but why not experiment with a few different colors and see how they look and in conjunction with other colors until you come up with a match. Only a small area but nice to get it just right first go. Good luck