Is there an extra fee for charging to your room?

Caesers add a $35 per night resort fee,that covers internet/gym etc

No extra charge for charging to room other then what you are charging to it and the overall resort fee.

i am not sure let might charge

There's an overall resort fee. But no additional fee for room charge in my experience.

Over what amount do they add a gratuity?

No but over a certain amount they add gratuity

I didn't stay at Ceasars but usually the Vegas hotels will take an additional deposit upon check in to cover any room charges.

I don't kmow