If you look at the link I posted you will have your questions about what greens rabbits like and should eat answered. He really should be eating a lot more greens!
No even a little pinch of sugar in the water is not good for him. Sugar causes a lot of rabbits’ digestive issues, please don’t give him any. A good balanced diet that includes fruits and vegetables is still careful to keep sugar low! And to be honest your rabit does not have a good diet, adding any sugar to it will not be helping him.
The best kind of pellets are made up mostly of timothy hay, it is the main ingredient. If you look in the store attached to this forum (Binky Bunny) you will see some of the best brands of pellets, and read about why they are good. You can order pellets online so you may want to think about doing that. Chickens needs are Very Different from a rabbits, chickens do not need hay, and they do need grain, while your rabbit Does Need Hay, and Should NOT have grain. I am sure you care about him so you may really want to think/find some ways of making things better for him. if he starts eating good pellets, hay and more greens I suspect you will be surprised at what a different rabbit you have.
But going back to your original question, hay itself is important, keeps their teeth healthy and digestive system functioning properly so you do need to try to get him eating it. Hopefully some of the members who are closer to you in the world will have some other suggestions about specific kinds. But please read the article I posted for you last time, it would really help you and your rabbit to know what he needs!!!