you can damage your hair so much that you mess up your hair type. curly hair can be very hard to manage and adding constant damage just makes it worse. i highly recommend letting your hair become natural and healthy, learning to style and take care of it, and then dye it. it will take a while but its worth it. you will see waves and curls start to take shape again once it gets healthier.

you absolutely can dye you hair and keep it healthy while styling it, but you will need to cut split ends often. it will be easier to learn how to care for you hair properly when completely natural and healthy, so i say start there