I think a comfortable distance between the island and the counter is around 42". It seems that you have only 30" between your cook top and the counter. I might be a little too tight. The wall between the entrance and the kitchen could be 4' long instead of 6', you would then be able to move the island a foot which would give you more room between the cook top and the island. Could you switch the location of the toilet and vanity in your dad's bathroom so your enter facing a vanity instead of a toilet which is a lot nicer.

I think you should stay with a simple pattern for draperies. Possibly a pattern incorporating the white trim and warm yellow walls. This would be soft and understated and something that you wouldn't get tired of easily. Other colors could be introduced with accessories.

Most my doors were already here, but I did have one moved over, about 6 inches. However, the entire space was demo'd, and rebuilt, so that's not the best example to draw from. If you want the door hidden, in a pocket, yes, you will need a skilled carpenter. Essentially, the opening header and frame, will become twice it's size, with the "pocket" part, hidden behind the wall. The studs/supports will need to be removed to make a space for the door to slide into. Do you have any switches or outlets on the fireplace wall?

How do you decorate your place, what kind of style, colors, and feelings? That will greatly influence the type of door you might want. Also, think of your budget, and whether you want to install it yourself or hire a professional (you don't need to tell us, just keep that in mind). Then look around Houzz, in the products page, they have lots of interior sliding doors and hinged ones, from elegant frosted glass in a dark wood frame, to rustic reclaimed wood planks. You may not want to purchase that exact model, but it might give you a better idea of what would fulfill your airflow needs without sacrificing style.