It seems the WC would be better on the top wall with the vanity. If you have a walk-in shower, it doesn't need to be quite so wide, and you can move the entrance to the bottom to be more generous. If you have a tub/shower combo, you don't need the partition at all. Consider flipping the door swing unless you're really concerned with privacy.

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.

hi , i have designed more than 60 kitchens and with my experience it's extremely difficult to cook with stove in the corner of moved a bit to the right it would end up too close to the sink if the space is less and whatever you wash there are chances that it may fall into the cooking bowl .it would really help if you let me know the measurements of that wall . If you want to try something new you can check out cooking corner solution famous in European countries

Just because you want to use the space below the stairs, do not just add drawers or shelfs unless you reaalllyyy need it. I would suggest go for adding something green to your house. Its healthy by adding air purifying plants. These plants are nowadays available in most of the nurseries and moreover Green patch in the house gives a beautiful look to the house and is also good for eyes ( the green color). Below are few picture to motivate you for Green patch or Indoor garden.