Can ROTC cadets who are Green to Gold negotiate airborne and ranger school into their contract?

No, it's not a reenlistment contract, it's ROTC. The Army is paying for your school, you owe them, not the other way around.
Plus, it's not that kind of contract. Depending on how you branch and where you end up, there will be plenty of opportunities to volunteer for Airborne and then Ranger.

No. ( sorry I laughed at this) As a cadet you have negative power or control. You're only guarantee as a cadet IF you get a enrollment allocation ( slip of paper sending you to officer training) is that you will be an officer if you complete the program.

NEEDS OF THE MILITARY, reign supreme

They do not have to agree to give you any position type. Example : I was a scholarship cadet Middle Eastern Studies and the USAF paid for my education and picked my major; when I commissioned they needed space officers...guess what I became. A non deployable technical field officer. It is what it is. Different world entirely, you have ALOT less choice on field assignments as a GOLD.

No, that is not possible. You are signing a completely different contract. However, you can compete for any of the schools your program has slots for. There are airborne, air assault, jungle warfare, northern warfare, etc. More than likely you will be put on an OML where your grades and fitness level will be most important. If Ranger School is a goal, strive to be an Infantry officer as that will give you the best way to get there. But nothing is guaranteed in a contract, you will have to earn it all. Good luck!