I don't love word art, so I'd remove both pieces and hang some curtains to soften the windows and add depth. The rug is a little big for the space, especially with the mat layering over it. A new light fixture, doesn't have to be super fancy, would really help too. As for paint, seeing the kitchen would help.

I hung curtains, but I feel it is too much for this small nook.

Are there color you like for paint? What colors are in your kitchen?

for shades you might want to check Etsy

https://www.etsy.com/search?q=roman%20shades

Yes to a circular show stopping chandelier as a focal point for the space. I like the high hung roman shades too. It would be helpful to see pics of the rest of the kitchen to know if or what call color to go with.

Check out ruggable.com for washable pet/kid friendly rugs. Anything hung on walls should center 5' above the floor. Steer clear of "word art" as it is past its prime! Faux roman shades in fabric would do well here; soft pattern and color but up out of the way of sticky hands.

Sure you can.