Yes. While the grantor was alive the trust reported under the grantor's Social Security number. At death it becomes irrevocable and a separate taxpayer, so it needs an employer identification number to open or retitle accounts and to file its income tax return. The EIN application prepares IRS Form SS-4 for a trust.
The trust document or a certification of trust, the death certificate, the trustee's identification, and the trust's EIN. Each institution publishes its own list, and the letter of instruction follows the list of the bank, brokerage, or insurer it is addressed to.
Not for the trust's assets. Property titled in the trust passes under the trust document without a court case. Property left outside the trust passes under the pour-over will, and where that property exceeds the state's small estate limit, the executor named in that will opens a probate case for it using the probate forms.
Each online service runs its own program for a deceased user's account, with its own request form, document list, and rules on what can be released. The digital assets recovery letter is built to the program of the service it is addressed to and requests the account, balance, or points under that program.