This is way too complicated for an internet post. There are other options as well. It depends on what she wants and how advanced the disease is.

So the same lawyer handling the real estate transfer should handle the trust issues. The answer is whether the trust has a tax ID number already. ...

Your post is a little unclear on what the will says. I am not sure who "she" is. If it is the judge, and the trust is not part of the will, then...

No, because revocable trusts are not true trusts, and use the grantor's SSN. An irrevocable trust gets its own TIN.

In trying to do it yourself, the errors and delay have caused you to be on the verge of being out-maneuvered. If you have siblings, they are going...

If your letters are unrestricted, then yes.

A lawyer can issue a subpoena. You cannot. Thus, you need to prepare the subpoena form pro se to be issued by the Surrogate.

No. You do not need to do anything. Hold onto the will in case something comes up someday.

File for voluntary administration and bring letters from Surrogate court to dmv.

You cannot check if he left a will. You can check if one was filed in the county of residence of death by calling the Surrogate’s Court.