Just under the cornice, use same rod height for all openings even though doors are shorter.

I usually add glass between the wood and vanity. You can add a layer of stone or marble if you wish

I think this kitchen is functional because there's handles for the drawers!

You are so right white is never out of fashion. I would set your budget and then look at your options. If you plan to stay in the house for many years then spend to the top of your budget (if that is going to give you a life time of pleasure), if you plan on being at the home for only a short time / few years then I would go mid range so it looks lovely, will have good resale value but you can invest your well earned money to go towards something else as well. Obviously Marble / Granite is the top of the range but there are so many cheaper and very attractive options these days that look just as good.