I'm taking it that these are ready made/ready to hang? And are a pair? If so then yeah they should be fine so long as you have the room on either side of your window for the overhang.

almost anything is possible but depending on what the drawers will be part of a compromise could be cheaper...eg some vanity cupboards could have drawers that shallow but kitchens and wardrobes are usually deeper..,,what are you planning to store? would 40cm deep open shelves with free standing baskets be suitable?

for a comfortable walking space the island should be about 1200mm - 1500mm away from the long side to the other counters and at least 900mm -1200mm from the end to any other counter or wall then the island could be 600mm deep and 900mm long to fit your cooktop BUT the cooktop on such a small island would not be very safe to use (unless you live alone and have no visitors) and there should be much better options....post a plan of the whole room with measurements and a list of everything you need to fit in the whole room

We agree, a rug could help define and delineate the different spaces! It looks like you may need some specific and quite large sizes - look for rugs that can be ordered in custom sizes to take the stress out of trying to make stock rugs fit! You have an absolutely amazing artwork on the wall there - perhaps use these blues and golden tones as inspiration? Blues would looks great with the wooden cupboards and accents. Some suggestions: https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/aegean-sky-blue/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/dover-light-blue/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/mars-light-blue/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/morgan-grey-2/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/soraya/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/venus-beige/ https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/twill-blue/ https://www.designerrugs.com.au/rug-collections/designer-collaborations/akira-isogawa-hirameki/batik-ubud/