Can a soldier be denied terminal leave for 30 days?

Yes they can. Not likely unless there is a unit mission that requires there presence.

Yes it can. Terminal/Transitional Leave is just a term used for the leave days saved up prior to ETS. It's still Leave. And still subject to the approval/disapproval of the Commander. It can also be yanked by the Commander even after it's been approved. I discovered that first hand in Germany many years ago.

Yes. But when in doubt AR 600-8-10 is always a friend. Make sure you out process completely as well. I personally was put in an AWOL status because I missed one signature. Leave was turned in, and I signed out, but the mistake wasn’t caught until about 2 weeks into my “terminal “ leave. I had to come back, serve the remaining days I was “awol” for. Then properly released. Just cross your t’s and dot your I’s. I had to wing it trying to final out. Hopefully you get more guidance. Good luck!