It doesn't seem totally clear to me what is going on here. The answer to (1) depends on what power the Dean has. If the Dean
is the only one who really has the power to an extend an offer of any kind (oral or written), then you must wait for the Dean to negotiate. However, at bigger schools, chairs often have this power. I would go back to the chair and say something like "I have a couple of concerns about "X", should I address those now or should I wait for the Dean?"
Regarding (2), most places give a week or two. And yes, you can try rescheduling, but don't push it. If someone resists, then best to go with the original timing and make the best of this difficult situation.
As far as (3) goes, I don't think an offer would get pulled just because you are negotiating, but yes, I think there are cases where one party or another gets exasperated, and just pulls out of the process. I..e., the offer effectively goes away because acceptable terms can not be met.
My questions regarding the current situation are:
(1) Is it now the right time to negotiation? Or should I wait till the official offer letter is in hands?
(2) How long do they usually give for considering the offer? If no enough time, is it appropriate to let the to-go university know and ask for an earlier interview?
(3) Is it possible that a university takes back an offer because the candidate asks too much during negotiation?
Thanks for your information in advance.